Deck 8: Hypothesis Testing

Question 1

Solve the problem.
What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether the event is likely. Claim: An employee of a company is equally likely to take a sick day on any day of the week. Last year, the total number of sick days taken by all the employees of the company was 143. Of these, 52 were Mondays, 14 were Tuesdays, 17 were Wednesdays, 17 were Thursdays, and 43 were Fridays.

Answer 1

If the employees were equally likely to take sick days on any day of the week, the probability of
obtaining such a distribution of sick days would be extremely small. Therefore, by the rare event rule, we
conclude that the claim that an employee of the company is equally likely to take a sick day on any day of
the week is probably not correct.

Question 2

Solve the problem.
Write the claim that is suggested by the given statement, then write a conclusion about the claim. Do not use symbolic expressions or formal procedures; use common sense. A math teacher tries a new method for teaching her introductory statistics class. Last year the mean score on the final test was 73. This year the mean on the same final was 76.

Answer 2

The claim is that the new teaching method is more effective than the old method and that on average
students will score higher when she uses the new teaching method than when she uses the old teaching
method. The small difference in the two means is not strong evidence that the new method is more
effective. Even if both methods were equally effective, such a difference could easily occur by chance.

Question 3

Provide an appropriate response.
Describe how to write the null and alternative hypotheses based on a claim. You may give an example to clarify your explanation.

Answer 3

Write the claim symbolically. Then write its complementary statement. The null hypothesis contains the
statement of equality, and the alternate hypothesis contains the other.

Question 4

Provide an appropriate response.
Suppose the claim is in the alternate hypothesis. What form does your conclusion take? Suppose the claim is in the null hypothesis. What form does your conclusion take?

Question 5

Write the claim that is suggested by the given statement, then write a conclusion about the claim. Do not use symbolic expressions or formal procedures; use common sense. Of a group of 1000 people suffering from arthritis, 500 receive acupuncture treatment and 500 receive a placebo. Among those in the placebo group, 24% noticed an improvement, while of those receiving acupuncture, 44% noticed an improvement.

Question 6

Complete the following table on hypothesis testing. $$\begin{array} { c | l | l } \text { Test about } & \text { Distribution } & \text { Assumptions } \\\hline \text { Mean } & & \\\\\text { Mean } & & \\\\\text { Proportion } & & \\\\\text { Variance } & & \\\\\end{array}$$

Question 7

Solve the problem.
Write the claim that is suggested by the given statement, then write a conclusion about the claim. Do not use symbolic expressions or formal procedures: use common sense. A person claims to have extra sensory powers. A card is drawn at random from a deck of cards and without looking at the card, the person is asked to identify the suit of the card. He correctly identifies the suit 28 times out of 100.

Question 8

What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether the event is likely. Claim: A roulette wheel is fair and in 40 consecutive spins of the wheel, black shows up 23 times. (A roulette wheel has 38 equally likely slots of which 18 are black).

Question 9

Solve the problem.
What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether the event is likely. Claim: A die is fair and in 100 rolls there are 63 sixes.

Question 10

Provide an appropriate response.
Compare the steps in the traditional method of hypothesis testing with the steps in the P-value method of hypothesis testing. How are they alike and how are they different?

Question 11

Provide an appropriate response.
Explain how to determine if a hypothesis test is one-tailed or two-tailed and explain how you know where to shade the critical region. Give an example for each which includes the claim, the hypotheses, and the diagram with the critical region shaded.

Question 12

Write the claim that is suggested by the given statement, then write a conclusion about the claim. Do not use symbolic expressions or formal procedures; use common sense. Last year an appliance manufacturer received many complaints about the high rate of defects among its washing machines. Approximately 9% of the machines were defective in some way. This year the company tightened up its quality control procedures. The latest shipment of 250 washing machines contained 2 defectives.

Question 13

Complete the table to compare the z and t distributions. $$\begin{array} { c | c | c } & \mathrm { z } \text { distribution } & \mathrm { t } \text { distribution } \\\hline \text { Shape } & & \\\\\text { Mean value } & & \\\\\text { Standard deviation value } & & \\\\\text { Requirements } & &\end{array}$$

Question 14

Discuss the rationale for hypothesis testing. Refer to the comparison of the assumption and the sample results.

Question 15

Provide an appropriate response.
List three phrases which are associated with one-tailed claims.

Question 16

Solve the problem.
What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether the event is likely. Claim: A company claims that the proportion of defectives among a particular model of computers is 4%. In a shipment of 200 such computers, there are 10 defectives.

Question 17

Provide an appropriate response.
Define Type I and Type II errors. Give an example of a Type I error which would have serious consequences. Give an example of a Type II error which would have serious consequences. What should be done to minimize the consequences of a serious Type I error?

Question 18

Define P-values. Explain the two methods of interpreting P-values.

Question 19

Provide an appropriate response.
When testing hypotheses about a mean, the decision must be made as to the distribution to be used. Discuss the decision process used to decide whether z or t or neither is the proper distribution.

Question 20

Provide an appropriate response.

Question 21

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.

- $\alpha = 0.08 ; H _ { 1 }$ is $\mu \neq 3.24$

A) $1.75$
B) $\pm 1.75$
C) $1.41$
D) $\pm 1.41$

Question 22

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter.

-Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Use $\mu$ , the true average mileage of the Libra.

A) $\begin{array}{l}\mathrm{H}_{0}: \mu=30 \\\mathrm{H}_{1}: \mu>30\end{array}$

B) $\begin{array}{l}\mathrm{H}_{0}: \mu<30 \\\mathrm{H}_{1}: \mu \geq 30\end{array}$

C) $\begin{array}{l}\mathrm{H}_{0}: \mu>30 \\\mathrm{H}_{1}: \mu \leq 30\end{array}$

D) $\begin{array}{l}H_{0}: \mu=30 \\H_{1}: \mu<30\end{array}$

Question 23

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter.

-A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, $p$ , is less than 2 in every one thousand.

A) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}<0.002 \\\mathrm{H}_{1}: \mathrm{p} \geq 0.002\end{array}$

B) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}=0.002 \\\mathrm{H}_{1}: \mathrm{p}>0.002\end{array}$

C) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}=0.002 \\\mathrm{H}_{1}: \mathrm{p}<0.002\end{array}$

D) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}>0.002 \\\mathrm{H}_{1}: \mathrm{p} \leq 0.002\end{array}$

Question 24

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter.

-A psychologist claims that more than 6.3 percent of the population suffers from professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from extreme shyness.

A) $\begin{array}{l}\mathrm{H}_{0}: p<6.3 \% \\\mathrm{H}_{1}: \mathrm{p} \geq 6.3 \%\end{array}$

B) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}=6.3 \% \\\mathrm{H}_{1}: \mathrm{p}<6.3 \%\end{array}$

C) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}=6.3 \% \\\mathrm{H}_{1}: \mathrm{p}>6.3 \%\end{array}$

D) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}>6.3 \% \\\mathrm{H}_{1}: \mathrm{p} \leq 6.3 \%\end{array}$

Question 25

$$\text { Find the value of the test statistic } z \text { using } z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } } \text {. }$$

-A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n = 1158 subjects with 30% saying that they play a sport.

A)27.78
B)13.61
C)-27.78
D)-13.61

Question 26

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter.

-The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, $\mu$ , of $48 ^ { \circ } \mathrm { F }$ , ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.

A) $\begin{array}{l}\mathrm{H}_{0}: \mu \geq 48^{\circ} \\\mathrm{H}_{1}: \mu<48^{\circ}\end{array}$

B) $\begin{array}{l}\mathrm{H}_{0}: \mu=48^{\circ} \\\mathrm{H}_{1}: \mu \neq 48^{\circ}\end{array}$

C) $\begin{array}{l}\mathrm{H}_{0}: \mu \neq 48^{\circ} \\\mathrm{H}_{1}: \mu=48^{\circ}\end{array}$

D) $\begin{array}{l}\mathrm{H}_{0}: \mu \leq 48^{\circ} \\\mathrm{H}_{1}: \mu>48^{\circ}\end{array}$

Question 27

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter.

-A researcher claims that $62 \%$ of voters favor gun control.

A) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p} \geq 0.62 \\\mathrm{H}_{1}: \mathrm{p}<0.62\end{array}$

B) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}<0.62 \\\mathrm{H}_{1}: \mathrm{p} \geq 0.62\end{array}$

C) $\begin{array}{l}H_{0}: p \neq 0.62 \\H_{1}: p=0.62\end{array}$

D) $\begin{array}{l}H_{0}: p=0.62 \\H_{1}: p \neq 0.62\end{array}$

Question 28

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter.

-The owner of a football team claims that the average attendance at games is over 67,800, and he is therefore justified in moving the team to a city with a larger stadium.

A) $\mathrm{H}_{0}: \mu$ , the average attendance at games, is less than 67,800
$\mathrm{H}_{1}: \mu$ , the average attendance at games, is greater than or equal to 67,800

B) $\mathrm{H}_{0}: \mu$ , the average attendance at games, is greater than 67,800
$\mathrm{H}_{1}: \mu$ , the average attendance at games, is less than or equal to 67,800

C) $\mathrm{H}_{0}: \mu$ , the average attendance at games, is equal to 67,800
$\mathrm{H}_{1}: \mu$ , the average attendance at games, is greater than 67,800

D) $\mathrm{H}_{0}: \mu$ , the average attendance at games, is equal to 67,800
$\mathrm{H}_{1}: \mu$ , the average attendance at games, is less than 67,800

Question 29

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.

- $\alpha = 0.1$ for a two-tailed test.

A) $\pm 1.4805$
B) $\pm 1.645$
C) $\pm 2.33$
D) $\pm 2.052$

Question 30

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter.

-The principal of a middle school claims that test scores of the seventh-graders at her school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by $\sigma = 14.7$ .

A) $\begin{array}{l}\mathrm{H}_{0}: \sigma=14.7 \\\mathrm{H}_{1}: \sigma<14.7\end{array}$

B) $\begin{array}{l}\mathrm{H}_{0}: \sigma=14.7 \\\mathrm{H}_{1}: \sigma>14.7\end{array}$

C) $\begin{array}{l}\mathrm{H}_{0}: \sigma<14.7 \\\mathrm{H}_{1}: \sigma>14.7\end{array}$

D) $\begin{array}{l}H_{0}: \sigma>14.7 \\H_{1}: \sigma \leq 14.7\end{array}$

Question 31

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.

- $\alpha = 0.05$ for a two-tailed test.

A) $\pm 2.575$
B) $\pm 1.96$
C) $\pm 1.645$
D) $\pm 1.764$

Question 32

Use the given information to find the P-value

-The test statistic in a right-tailed test is z = 1.43.

A)0.4236
B)0.0434
C)0.0764
D)0.5000

Question 33

Use the given information to find the P-value

-The test statistic in a left-tailed test is z = -1.83.

A)0.0336
B)0.4326
C)0.4232
D)0.0443

Question 34

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter.

-An entomologist writes an article in a scientific journal which claims that fewer than 11 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.

A) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}>0.0011 \\\mathrm{H}_{1}: \mathrm{p} \leq 0.0011\end{array}$ )

B) $\begin{array}{l}H_{0}: p=0.0011 \\H_{1}: p>0.0011\end{array}$

C) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}<0.0011 \\\mathrm{H}_{1}: \mathrm{p} \geq 0.0011\end{array}$

D) $\begin{array}{l}\mathrm{H}_{0}: \mathrm{p}=0.0011 \\\mathrm{H}_{1}: \mathrm{p}<0.0011\end{array}$

Question 35

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter.

-A cereal company claims that the mean weight of the cereal in its packets is at least $14 \mathrm { oz }$ .

A) $\begin{array}{l}\mathrm{H}_{0}: \mu>14 \\\mathrm{H}_{1}: \mu \leq 14\end{array}$

B) $\begin{array}{l}H_{0}: \mu=14 \\H_{1}: \mu>14\end{array}$

C) $\begin{array}{l}\mathrm{H}_{0}: \mu<14 \\\mathrm{H}_{1}: \mu \geq 14\end{array}$

D) $\begin{array}{l}H_{0}: \mu=14 \\H_{1}: \mu<14\end{array}$

Question 36

Use the given information to find the P-value

-The test statistic in a left-tailed test is z = -2.05.

A)0.0202
B)0.0453
C)0.4798
D)0.5000

Question 37

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.

- $\alpha = 0.09$ for a right-tailed test.

A) $\pm 1.34$
B) $+ 1.96$
C) $\pm 1.96$
D) $+ 1.34$

Question 38

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z
value used to test a null hypothesis.
The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 647 drowning deaths of children with 30% of them attributable to beaches.

A)2.94
B)-2.94
C)-2.78
D)2.78

Question 39

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of
the test statistic that would result in rejection of the null hypothesis.

-A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the $\sigma = 3.3 \mathrm { mg }$ claimed by the manufacturer.

A) $\begin{array}{l}\mathrm{H}_{0}: \sigma \leq 3.3 \mathrm{mg} \\\mathrm{H}_{1}: \sigma>3.3 \mathrm{mg}\end{array}$

B) $\begin{array}{l}\mathrm{H}_{0}: \sigma=3.3 \mathrm{mg} \\\mathrm{H}_{1}: \sigma \neq 3.3 \mathrm{mg}\end{array}$

C) $\begin{array}{l}\mathrm{H}_{0}: \sigma \neq 3.3 \mathrm{mg} \\\mathrm{H}_{1}: \sigma=3.3 \mathrm{mg}\end{array}$

D) $\begin{array}{l}\mathrm{H}_{0}: \sigma \geq 3.3 \mathrm{mg} \\\mathrm{H}_{1}: \sigma<3.3 \mathrm{mg}\end{array}$

Question 40

Use the given information to find the P-value

-The test statistic in a right-tailed test is z = 0.52.

A)0.1915
B)0.3015
C)0.1950
D)0.5530

Question 41

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Identify the type I error for the test.

A)The error of rejecting the claim that the true proportion is less than 16 in ten thousand when it really is less than 16 in ten thousand.
B)The error of rejecting the claim that the true proportion is at least 16 in ten thousand when it really is at least 16 in ten thousand.
C)The error of failing to reject the claim that the true proportion is at least 16 in ten thousand when it is actually less than 16 in ten thousand.

Question 42

Use the given information to find the P-value

-The test statistic in a two-tailed test is z = -1.63.

A)0.1253
B)0.6783
C)0.1032
D)0.4372

Question 43

Carter Motor Company claims that its new sedan, the Libra, will average better than 19 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is sufficient evidence to support the claim that the mean is greater than 19 miles per gallon.
B)There is not sufficient evidence to support the claim that the mean is greater than 19 miles per gallon.
C)There is not sufficient evidence to support the claim that the mean is less than 19 miles per gallon.
D)There is sufficient evidence to support the claim that the mean is less than 19 miles per gallon.

Question 44

An entomologist writes an article in a scientific journal which claims that fewer than 19 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient evidence to support the claim that the true proportion is less than 19 in ten thousand.
B)There is not sufficient evidence to support the claim that the true proportion is greater than 19 in ten thousand.
C)There is sufficient evidence to support the claim that the true proportion is less than 19 in ten thousand.
D)There is sufficient evidence to support the claim that the true proportion is greater than 19 in ten thousand.

Question 45

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-Carter Motor Company claims that its new sedan, the Libra, will average better than 23 miles per gallon in the city. Identify the type I error for the test.

A)The error of rejecting the claim that the true proportion is more than 23 miles per gallon when it really is more than 23 miles per gallon.
B)The error of rejecting the claim that the mean is at most 23 miles per gallon when it really is at most 23 miles per gallon.
C)The error of failing to reject the claim that the mean is at most 23 miles per gallon when it is actually greater than 23 miles per gallon.

Question 46

A psychologist claims that more than 75 percent of the population suffers from professional problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient evidence to support the claim that the true proportion is greater than 75 percent.
B)There is sufficient evidence to support the claim that the true proportion is greater than 75 percent.
C)There is sufficient evidence to support the claim that the true proportion is less than 75 percent.
D)There is not sufficient evidence to support the claim that the true proportion is less than 75 percent.

Question 47

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is sufficient evidence to warrant rejection of the claim that the mean weight is at least 14 oz.
B)There is not sufficient evidence to warrant rejection of the claim that the mean weight is less than 14 oz.
C)There is not sufficient evidence to warrant rejection of the claim that the mean weight is at least 14 oz.
D)There is sufficient evidence to warrant rejection of the claim that the mean weight is less than 14 oz.

Question 48

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by $$\sigma = 14.7$$ Identify the type I error for the test.

A)The error of rejecting the claim that the standard deviation is less than 14.7 when it really is less than 14.7.
B)The error of failing to reject the claim that the standard deviation is at least 14.7 when it is actually less than 14.7.
C)The error of rejecting the claim that the standard deviation is at least 14.7 when it really is at least 14.7.

Question 49

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 3 in every ten thousand. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient evidence to support the claim that the true proportion is less than 3 in ten thousand.
B)There is sufficient evidence to support the claim that the true proportion is greater than 3 in ten thousand.
C)There is not sufficient evidence to support the claim that the true proportion is greater than 3 in ten thousand.
D)There is sufficient evidence to support the claim that the true proportion is less than 3 in ten thousand.

Question 50

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 1 in every one thousand. Identify the type II error for the test.

A)The error of rejecting the claim that the true proportion is at least 1 in one thousand when it really is at least 1 in one thousand.
B)The error of rejecting the claim that the true proportion is less than 1 in one thousand when it really is less than 1 in one thousand.
C)The error of failing to reject the claim that the true proportion is at least 1 in one thousand when it is actually less than 1 in one thousand.

Question 51

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, $\mu$ , of $45 ^ { \circ } \mathrm { F }$ , ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is not sufficient evidence to support the claim that the mean temperature is equal to $45 ^ { \circ } \mathrm { F }$ .
B) There is not sufficient evidence to support the claim that the mean temperature is different from $45 ^ { \circ } \mathrm { F }$ .
C) There is sufficient evidence to support the claim that the mean temperature is equal to $45 ^ { \circ } \mathrm { F }$ .
D) There is sufficient evidence to support the claim that the mean temperature is different from $45 ^ { \circ } \mathrm { F }$ .

Question 52

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-A psychologist claims that more than 3 percent of the population suffers from professional problems due to extreme shyness. Identify the type II error for the test.

A)The error of rejecting the claim that the true proportion is at most 3 percent when it really is at most 3 percent.
B)The error of rejecting the claim that the true proportion is more than 3 percent when it really is more than 3 percent.
C)The error of failing to reject the claim that the true proportion is at most 3 percent when it is actually more than 3 percent.

Question 53

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-A researcher claims that 62% of voters favor gun control. Identify the type II error for the test.

A)The error of failing to reject the claim that the proportion favoring gun control is 62% when it is actually different than 62%.
B)The error of rejecting the claim that the proportion favoring gun control is more than 62% when it really is more than 62%.
C)The error of rejecting the claim that the proportion favoring gun control is 62% when it really is less than 62%.

Question 54

The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by $\sigma = 14.7$ .
Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is not sufficient evidence to support the claim that the standard deviation is less than 14.7.
B) There is sufficient evidence to support the claim that the standard deviation is less than 14.7.
C) There is sufficient evidence to support the claim that the standard deviation is greater than $14.7$ .
D) There is not sufficient evidence to support the claim that the standard deviation is greater than $14.7$ .

Question 55

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-The owner of a football team claims that the average attendance at games is over 60,000, and he is therefore justified in moving the team to a city with a larger stadium. Identify the type II error for the test.

A)The error of rejecting the claim that the mean attendance is at most 60,000, when it really is at most 60,000.
B)The error of failing to reject the claim that the mean attendance is at most 60,000, when it is actually greater than 60,000.
C)The error of failing reject the claim that the mean attendance is more than 60,000, when it is actually less than 60,000.

Question 56

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, $\mu$ , of $50 ^ { \circ } \mathrm { F }$ , ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Identify the type I error for the test.

A) The error of failing to reject the claim that the mean temperature equals $50 ^ { \circ } \mathrm { F }$ when it is really different from $50 ^ { \circ } \mathrm { F }$ .
B) The error of rejecting the claim that the mean temperature equals $50 ^ { \circ } \mathrm { F }$ when it really does equal $50 ^ { \circ } \mathrm { F }$ .
C) The error of rejecting the claim that the mean temperature equals $50 ^ { \circ } \mathrm { F }$ when it is really different from $50 ^ { \circ } \mathrm { F }$ .

Question 57

A researcher claims that 62% of voters favor gun control. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is sufficient evidence to support the claim that more than 62% of voters favor gun control.
B)There is not sufficient evidence to support the claim that 62% of voters favor gun control.
C)There is sufficient evidence to warrant rejection of the claim that 62% of voters favor gun control.
D)There is not sufficient evidence to warrant rejection of the claim that 62% of voters favor gun control.

Question 58

The owner of a football team claims that the average attendance at games is over 727, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is sufficient evidence to support the claim that the mean attendance is greater than than 727.
B)There is not sufficient evidence to support the claim that the mean attendance is less than 727.
C)There is sufficient evidence to support the claim that the mean attendance is less than 727.
D)There is not sufficient evidence to support the claim that the mean attendance is greater than 727.

Question 59

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the $\sigma = 3.3 \mathrm { mg }$ claimed by the manufacturer. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is sufficient evidence to support the claim that the standard deviation is different from $3.3 \mathrm { mg }$ .
B) There is sufficient evidence to support the claim that the standard deviation is equal to $3.3 \mathrm { mg }$ .
C) There is not sufficient evidence to support the claim that the standard deviation is different from $3.3 \mathrm { mg }$ .
D) There is not sufficient evidence to support the claim that the standard deviation is equal to $3.3$ mg.

Question 60

Use the given information to find the P-value

-The test statistic in a two-tailed test is z = 1.95.

A)0.3415
B)0.0244
C)0.0512
D)0.4423

Question 61

Suppose that you perform a hypothesis test regarding a population mean, and that the evidence does not warrant rejection of the null hypothesis. When formulating the conclusion to the test, why is the phrase "fail to reject the null hypothesis" more accurate than the phrase "accept the null hypothesis"?

Question 62

Suppose that you wish to use a hypothesis test to test a claim made by a juice bottling company regarding the mean amount of juice in its 16 oz bottles. Why does the original claim sometimes become the null hypothesis, and why does it sometimes become the alternative hypothesis? Give an example of a claim which would become the null hypothesis and an example of a claim would become the alternative hypothesis.

Question 63

In a hypothesis test regarding a population mean, the probability of a type II error, $\beta ,$ , depends on the true value of the population mean.

Question 64

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

-In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief.

Question 65

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

-In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma. At the 0.05 significance level, test the claim that the proportion of all children in the town who suffer from asthma is 11%.

Question 66

Find the P-value for the indicated hypothesis test.
In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%.

A)0.2157
B)0.2843
C)0.5686
D)-0.2843

Question 67

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Identify the type I error for the test.

A)The error of failing to reject the claim that the mean weight is at least 14 oz. when it is really more than 14 oz.
B)The error of rejecting the claim that the mean weight is at least 14 oz. when it really is at least 14 oz.
C)The error of failing to reject the claim that the mean weight is at least 14 oz. when it is really less than 14 oz.

Question 68

Find the P-value for the indicated hypothesis test.
A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim.

A)0.1736
B)0.1591
C)0.3409
D)0.3264

Question 69

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

-A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, test the claim that at least half of all voters prefer the Democrat.

Question 70

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

-An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 234 fathers from Littleton yielded 96 who did not help with child care. Test the researcher's claim at the 0.05 significance level.

Question 71

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

-According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who would vote for the incumbent, test the claim that the actual percentage is 53%. Use a 0.10 significance level.

Question 72

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

-A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, test the manager's claim.

Question 73

Find the P-value for the indicated hypothesis test.
A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 32% of them plan to go into general practice. Find the P-value for a test of the school's claim.

A)0.1635
B)0.3078
C)0.1539
D)0.3461

Question 74

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

-A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a random sample of 600 disks, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier's claim that no more than 1% are defective.

Question 75

In a hypothesis test, an increase in ? will cause a decrease in the power of the test provided the sample size is kept fixed.

Question 76

Find the P-value for the indicated hypothesis test.
In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.

A)0.0524
B)0.0024
C)0.0262
D)0.0048

Question 77

Suppose that you are conducting a study on the effectiveness of a new teaching method and that you wish to use a hypothesis test to support your claim regarding the mean test score under this method. What restrictions are there in the wording of the claim? Will your claim become the null hypothesis or the alternative hypothesis, or does it depend on the situation? Give an example of a claim which is incorrectly worded.

Question 78

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

-A nationwide study of American homeowners revealed that $64 \%$ have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Can the value $0.64$ be rejected if a survey of 490 homes in Omaha yields 331 with one or more lawn mowers? Use ?=0.05

Question 79

In a hypothesis test, which of the following will cause a decrease in $\beta$ , the probability of making a type II error?
A: Increasing $\alpha$ while keeping the sample size $n$ , fixed
$B$ : Increasing the sample size $n$ , while keeping $\alpha$ fixed
$\mathrm { C }$ : Decreasing $\alpha$ while keeping the sample size $n$ , fixed
D: Decreasing the sample size $n$ , while keeping $\alpha$ fixed

A) B and C
B) C and D
C) A and B
D) A and D

Question 80

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test

-A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the $\sigma = 3.3$ claimed by the manufacturer. Identify the type II error for the test.

A)The error of rejecting the claim that the standard deviation is more than 3.3 mg when it really is more than 3.3 mg.
B)The error of failing to reject the claim that the standard deviation is 3.3 mg when it is actually different from 3.3 mg.
C)The error of rejecting the claim that the standard deviation is 3.3 mg when it really is 3.3 mg.