Question 1

Find the critical value or values of $\chi ^ { 2 }$ based on the given information.
-$\begin{array} { l } 
\mathrm { H } _ { 1 } : \sigma < 0.629 \
\mathrm { n } = 19 \
\alpha = 0.025
\end{array}$

Accepted Answer

A)  8.231 
B)  7.015 
C)  8.907 
D)  31.526 
A)  8.231 
B)  7.015 
C)  8.907 
D)  31.526

Question 2

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.

Accepted Answer

If the parent population is essentially

Question 3

Provide an appropriate response
-Tim believes that a coin is coming up tails less than $50 \%$ of the time. He tests the claim $p <$ $0.5$. In 100 tosses, the coin comes up tails 57 times. What is the value of the sample proportion? Do you think the P-value will be small or large and what should Tim conclude about the claim $p < 0.5$ ?

Accepted Answer

@#LAT-DLM&; The @#LAT-DLM&-value will be large. Ti

Question 4

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.

Accepted Answer

The claim is that the new teaching metho

Question 5

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

Accepted Answer

Write the claim symbolically.

Question 6

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

Accepted Answer

None

Question 7

Find the critical value or values of $\chi ^ { 2 }$ based on the given information.
-$\begin{array} { l } 
\mathrm { H } _ { 1 } : \sigma \neq 9.3 \
\mathrm { n } = 28 \
\alpha = 0.05
\end{array}$

Accepted Answer

A)  $- 14.573,14.573$ 
B)  $16.151,40.113$ 
C)  $- 40.113,40.113$ 
D)  $14.573,43.194$ 
A)  $- 14.573,14.573$ 
B)  $16.151,40.113$ 
C)  $- 40.113,40.113$ 
D)  $14.573,43.194$

Question 8

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the $\sigma = 3.3$ 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.

Accepted Answer

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

Question 9

The principal of a middle school claims that the standard deviation of the test scores of the seventh-graders at his school is less than 14.7. Identify the type I error for the test.

Accepted Answer

A)  Fail to reject the claim that the standard deviation is equal to 14.7 when it is actually less than 14.7. 
B)  Reject the claim that the standard deviation is equal to 14.7 when it is actually 14.7. 
C)  Fail to reject the claim that the standard deviation is equal to 14.7 when it is actually greater than 14.7. 
D)  Reject the claim that the standard deviation is equal to 14.7 when it is actually less than 14.7. 
A)  Fail to reject the claim that the standard deviation is equal to 14.7 when it is actually less than 14.7. 
B)  Reject the claim that the standard deviation is equal to 14.7 when it is actually 14.7. 
C)  Fail to reject the claim that the standard deviation is equal to 14.7 when it is actually greater than 14.7. 
D)  Reject the claim that the standard deviation is equal to 14.7 when it is actually less than 14.7.

Question 10

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.
-Various temperature measurements are recorded at different times for a particular city.
The mean of 20°C is obtained for 60 temperatures on 60 different days. Assuming that $\sigma = 1.5 ^ { \circ } \mathrm { C }$ test the claim that the population mean is 22°C. Use a 0.05 significance level.

Accepted Answer

@#LAT-DLM&. Test statistic: @#LAT-DLM&. P-value: @#LAT-DLM&. Because t

Question 11

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.

Accepted Answer

@#LAT-DLM&. Test statistic: @#LAT-DLM&. @#LAT-DLM&-value: @#LAT-DLM&.
Critical v

Question 12

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"?

Accepted Answer

In a hypothesis test, we do not prove th

Question 13

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
-A medical researcher claims that 12% of children suffer from a certain disorder. Identify the type I error for the test.

Accepted Answer

A)  Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 12% when that percentage is actually 12%. 
B)  Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 12% when that percentage is actually different from 12%. 
C)  Reject the claim that the percentage of children who suffer from the disorder is equal to 12% when that percentage is actually 12%. 
D)  Reject the claim that the percentage of children who suffer from the disorder is different from 12% when that percentage really is different from 12%. 
A)  Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 12% when that percentage is actually 12%. 
B)  Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 12% when that percentage is actually different from 12%. 
C)  Reject the claim that the percentage of children who suffer from the disorder is equal to 12% when that percentage is actually 12%. 
D)  Reject the claim that the percentage of children who suffer from the disorder is different from 12% when that percentage really is different from 12%.

Question 14

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected.
-When 12 bolts are tested for hardness, their indexes have a standard deviation of 41.7. Test the claim that the standard deviation of the hardness indexes for all such bolts is greater than 30.0. Use a 0.025 level of significance.

Accepted Answer

Test statistic: @#LAT-DLM&. Critical val

Question 15

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.

Accepted Answer

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

Question 16

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.

Accepted Answer

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

Question 17

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 defective units among a particular model of computers is 4%. In a shipment of 200 such computers, there are 10 defective units.

Accepted Answer

If the defective rate were really 4%, on

Question 18

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
-A manufacturer claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation of 3.3 mg. Identify the type II error for the test.

Accepted Answer

A)  Fail to reject the claim that the standard deviation is 3.3 mg when the standard deviation is actually equal to 3.3 mg. 
B)  Reject the claim that the standard deviation is 3.3 mg when it is actually different from 3.3 mg. 
C)  Fail to reject the claim that the standard deviation is 3.3 mg when the standard deviation is actually different from 3.3 mg. 
D)  Reject the claim that the standard deviation is 3.3 mg when it is actually equal to 3.3 mg. 
A)  Fail to reject the claim that the standard deviation is 3.3 mg when the standard deviation is actually equal to 3.3 mg. 
B)  Reject the claim that the standard deviation is 3.3 mg when it is actually different from 3.3 mg. 
C)  Fail to reject the claim that the standard deviation is 3.3 mg when the standard deviation is actually different from 3.3 mg. 
D)  Reject the claim that the standard deviation is 3.3 mg when it is actually equal to 3.3 mg.

Question 19

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim
-A random sample of 100 pumpkins is obtained and the mean circumference is found to be 40.5 cm. Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean circumference of all pumpkins is equal to 39.9 cm.

Accepted Answer

@#LAT-DLM&. Test statistic: @#LAT-DLM&. P-value: @#LAT-DLM&.

Question 20

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol $( \mu , p , \sigma )$ for the indicated parameter.
-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.

Accepted Answer

A) $\begin{array}{l} \mathrm{H}_{0}: \sigma \leq 3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma>3.3 \mathrm{mg} \end{array}$ B) $\begin{array}{l} \mathrm{H}_{0}: \sigma \geq 3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma<3.3 \mathrm{mg} \end{array}$ C) $\begin{array}{l} \mathrm{H}_{0}: \sigma \neq 3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma=3.3 \mathrm{mg} \end{array}$ D) $\begin{array}{l} \mathrm{H}_{0}: \sigma=3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma \neq 3.3 \mathrm{mg} \end{array}$ A) $\begin{array}{l} \mathrm{H}_{0}: \sigma \leq 3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma>3.3 \mathrm{mg} \end{array}$ B) $\begin{array}{l} \mathrm{H}_{0}: \sigma \geq 3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma<3.3 \mathrm{mg} \end{array}$ C) $\begin{array}{l} \mathrm{H}_{0}: \sigma \neq 3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma=3.3 \mathrm{mg} \end{array}$ D) $\begin{array}{l} \mathrm{H}_{0}: \sigma=3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma \neq 3.3 \mathrm{mg} \end{array}$

Find the critical value or values of $\chi ^ { 2 }$ based on the given information. - :\sigma<0.629 =19 \alpha=0.025

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.

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

Complete the table to compare the z and t distributions. z distribution t distribution Shape Mean value Standard deviation value Requirements

Find the critical value or values of $\chi ^ { 2 }$ based on the given information. - :\sigma9.3 =28 \alpha=0.05

The principal of a middle school claims that the standard deviation of the test scores of the seventh-graders at his school is less than 14.7. Identify the type I error for the test.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. -A medical researcher claims that 12% of children suffer from a certain disorder. Identify the type I error for the test.

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.

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.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. -A manufacturer claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation of 3.3 mg. Identify the type II error for the test.

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimates and Sample Size

Inferences From Two Samples

Correlation and Regression

Chi-Square and Analysis of Variance

Filters

Exam 8: Hypothesis Testing

Find the critical value or values of χ2\chi ^ { 2 }χ2 based on the given information. - :\sigma<0.629 =19 \alpha=0.025

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.

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

Complete the table to compare the z and t distributions. z distribution t distribution Shape Mean value Standard deviation value Requirements

Find the critical value or values of χ2\chi ^ { 2 }χ2 based on the given information. - :\sigma9.3 =28 \alpha=0.05

The principal of a middle school claims that the standard deviation of the test scores of the seventh-graders at his school is less than 14.7. Identify the type I error for the test.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. -A medical researcher claims that 12% of children suffer from a certain disorder. Identify the type I error for the test.

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

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

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. -A manufacturer claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation of 3.3 mg. Identify the type II error for the test.

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimates and Sample Size

Inferences From Two Samples

Correlation and Regression

Chi-Square and Analysis of Variance

Filters

Find the critical value or values of $\chi ^ { 2 }$ based on the given information. - :\sigma<0.629 =19 \alpha=0.025

Find the critical value or values of $\chi ^ { 2 }$ based on the given information. - :\sigma9.3 =28 \alpha=0.05

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.

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.