Deck 9: Statistical Hypothesis Testing: Hypothesis Tests for a Population Mean

Question 1

Which of the following is NOT a common step in hypothesis testing:

A)determine the null and alternative hypotheses
B)specify the level of significance $\alpha$
C)collect the sample data and compute the value of the test statistic
D)use $\alpha$ to determine the critical value and the rejection rule
E)compute the p-value based on the test statistic and compare it to $\beta$ to determine whether to reject H₀

Answer 1

compute the p-value based on the test statistic and compare it to $\beta$ to determine whether to reject H₀

Question 2

In hypothesis testing, the critical value is a number that establishes the boundary of the reject H₀ region of the test.

Answer 2

True

Question 3

When the p-value is used for hypothesis testing, the null hypothesis is rejected when the p-value < $\alpha$ .

Answer 3

True

Question 4

To decide whether to reject a null hypothesis about a population mean, a 95% confidence interval or two-tailed hypothesis test with a significance level of 2.5% could be used.

Question 5

A student believes that the average grade on the final examination in statistics is greater than 85.To make her case, she will take a sample of scores and test a skeptical null hypothesis.The correct set of hypotheses is

A)H₀: $\mu$ < 85; H_a: $\mu$ ≥ 85
B)H₀: $\mu$ > 85; H_a: $\mu$ ≤ 85
C)H₀: $\mu$ ≤ 85; H_a: $\mu$ > 85
D)H₀: $\mu$ = 85; H_a: $\mu$$\neq$ 85
E)none of the above

Question 6

In hypothesis testing, we reject the null hypothesis if the p-value > $\alpha$ .

Question 7

The p-value measures the probability that, if the null hypothesis is true, we would randomly produce a sample result at least as unlikely as the sample result that we actually produced.

Question 8

In hypothesis testing, we reject the null hypothesis if the p-value < $\alpha$ .

Question 9

In the standard forms for the null and alternative hypotheses, the equality part of a hypothesis can appear in either hypothesis.

Question 10

The level of significance in hypothesis testing is the probability of accepting a true null hypothesis.

Question 11

The magnitude of z for a two-tailed hypothesis test of a population mean is greater than it would be in a one-tail hypothesis test given the same level of significance.

Question 12

The probability of making a Type I error is typically denoted by $\beta$ .

Question 13

Which of the following does not need to be known in order to compute the p-value?

A)knowledge of whether the test is one-tailed or two-tailed
B)the value of the test statistic
C)the level of significance
D)a, b, and c are all unnecessary
E)a, b and c are all needed

Question 14

To decide whether to reject a null hypothesis about a population mean, a 95% confidence interval or two-tailed hypothesis test with a significance level of 5% could be used.

Question 15

Which of the following best describe(s) the significance level?

A)it is the probability of rejecting a true null hypothesis
B)it is denoted by $\alpha$
C)it is the probability of making a Type I error
D)it is used to define the boundary of the reject H₀ region
E)all of the above

Question 16

The level of significance, $\alpha$ is the probability of making a Type II error, which is rejecting a true null hypothesis.

Question 17

Type I error occurs when a false null hypothesis is rejected.

Question 18

The p-value is the probability associated with the test statistic while alpha $\alpha$ is the probability associated with the critical value.

Question 19

The level of significance in hypothesis testing, $\alpha$ , measures the maximum probability of making a Type II error, which is the probability of accepting a false null hypothesis.

Question 20

The value of the test statistic for a two-tail hypothesis test for a population mean is the same as for a one-tail hypothesis test.

Question 21

If a null hypothesis is rejected at a 1% significance level,

A)It may or may not be rejected at a 5% significance level.
B)It will not be rejected at a 5% significance level.
C)It will also be rejected at a 5% significance level.
D)The survey needs to be repeated in order to determine the conclusion at a 5% significance level.
E)none of the above

Question 22

In hypothesis testing, if the null hypothesis is rejected when the alternative hypothesis is true

A)a Type I error has been committed
B)a Type II error has been committed
C)either a Type I or Type II error has been committed
D)the correct decision has been made
E)none of the above

Question 23

A meteorologist stated that the average temperature during July in Orlando, Florida is exactly 80 degrees.A sample of 32 Julys was taken.If you wanted to challenge the statement, the correct set of hypothesis would be

A)H₀: $\mu$ < 80; H_a: $\mu$$\le$ 80
B)H₀: $\mu$$\le$ 80; H_a: $\mu$ > 80
C)H₀: $\mu$ = 80; H_a: $\mu$ $\neq$ 80
D)H₀: $\mu$$\neq$ 80; H_a: $\mu$ = 80
E)none of the above

Question 24

Which of the following is NOT a common step in hypothesis testing?

A)state the null and alternative hypotheses
B)use the significance level to establish the reject H₀ region of the test
C)compute the p-value for the sample result
D)apply the decision rule and make your decision
E)none of the above; all are steps

Question 25

Whenever the population standard deviation is unknown, which distribution is used in developing a hypothesis test for a population mean?

A)standard distribution
B)z distribution
C)binomial distribution
D)t distribution
E)none of the above

Question 26

A p-value is the

A)probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed
B)value of the test statistic
C)probability of a Type II error
D)probability corresponding to the critical value(s) in a hypothesis test
E)none of the above

Question 27

In hypothesis testing, the critical value is

A)a number that establishes the boundary of the reject H₀ region
B)the probability of a Type I error
C)the probability of a Type II error
D)the same as the p-value
E)none of the above

Question 28

When computing the p-value for a two-tailed hypothesis test, we need to

A)multiply two times the one-tail value
B)divide the upper p-value by two
C)multiply the $\alpha$ value by two
D)subtract the one-tail lower p-value from the one-tail upper p-value
E)none of the above

Question 29

Which of the following is NOT a common step in hypothesis testing?

A)state the null and alternative hypotheses
B)use the significance level to establish the decision rule
C)compute the value of the test statistic
D)apply the decision rule and make your decision
E)none of the above; all are common steps

Question 30

Changing the significance level of a hypothesis test from 5% to 10%,

A)Reduces the chances of Type I error.
B)Increases the chances of Type I error.
C)Reduces the chances of Type II error.
D)Both a and c are true.
E)Both b and c are true.

Question 31

If a null hypothesis is rejected at a 10% significance level,

A)It may or may not be rejected at a 5% significance level.
B)It will not be rejected at a 5% significance level.
C)It will be rejected at a 5% significance level.
D)The test needs to be repeated in order to determine the conclusion at a 5% significance level.
E)none of the above

Question 32

Type I error in hypothesis testing is

A)accepting the sample result when it should have been rejected
B)rejecting an alternative hypothesis that is actually false
C)rejecting a null hypothesis when it is actually true
D)rejecting the sample result when it should have been accepted
E)none of the above

Question 33

Which of the following is NOT a common step in hypothesis testing?

A)determine the p-value and compare it to $\alpha$
B)state the null and alternative hypothesis
C)use the significance level to establish the decision rule
D)compare the sample size to the population size
E)apply the decision rule and make your decision

Question 34

In hypothesis testing, the critical value is:

A)a number that establishes the boundary of the reject H₀ region
B)based on the significance level $\alpha$
C)compared to the test statistic to determine if the null hypothesis is rejected
D)all of the above
E)none of the above

Question 35

Type I error in hypothesis testing is

A)accepting a false null hypothesis
B)rejecting a true alternative hypothesis
C)rejecting a true null hypothesis
D)rejecting the sample result when it should have been accepted
E)none of the above

Question 36

When using the confidence interval approach for a two-tailed test, which of the following is true?

A)the rejection region is in the upper tail of the distribution
B)if the confidence interval contains the hypothesized value, then reject H₀
C)if the confidence interval contains the hypothesized value, do not reject the H₀
D)use the F distribution
E)none of the above

Question 37

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles.Management believes that due to a new production process, the life expectancy of its tires has increased.In order to convince others of the validity of management's belief, the correct set of hypotheses is

A)H₀: $\mu$ < 40,000; H_a: $\mu$ $\ge$ 40,000
B)H₀: $\mu$ $\le$ 40,000; H_a: $\mu$ > 40,000
C)H₀: $\mu$ > 40,000; H_a: $\mu$ $\le$ 40,000
D)H₀: $\mu$ $\ge$ 40,000; H_a: $\mu$ < 40,000
E)H₀: $\mu$ = 40,000; H_a: $\mu$ ≠ 40,000

Question 38

In hypothesis testing, the critical value is

A)a number that establishes the boundary of the reject H₀ region
B)based on the significance level $\alpha$
C)a and b only
D)the probability of a Type I error
E)used to set the p-value

Question 39

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink.Any over-filling or under-filling results in the shutdown and readjustment of the machine.To determine whether the machine is properly adjusted, the most appropriate set of hypotheses is

A)H₀: $\mu$ < 12; H_a: $\mu$ $\le$ 12
B)H₀: $\mu$$\le$ 12; H_a: $\mu$ > 12
C)H₀: $\mu$ = 12; H_a: $\mu$ $\neq$ 12
D)H₀: $\mu$ $\neq$ 12; H_a: $\mu$ = 12
E)none of the above

Question 40

The normal distribution can be used to approximate the t distribution when

A)standard deviations are small
B)sample size is large
C)the t distribution is skewed
D)a normal table is unavailable
E)none of the above

Question 41

You are to test the following hypotheses: H₀: µ ≥ 1200
H_a: µ < 1200
A sample of size 36 produces a sample mean of 1148, with a standard deviation of 160.The p-value for this test is

A).0512
B).0256
C).0334
D).0668

Question 42

You are to test the following hypotheses: H₀: µ ≥ 360
H_a: µ < 360
A sample of size 64 produces a sample mean of 348, with a standard deviation of 60.The p-value for this test is

A).0548
B).0274
C).1096
D).0438

Question 43

You are to test the following hypotheses: H₀: µ < 900
H_a: µ > 900
A sample of size 25 produces a sample mean of 926, with a standard deviation of 50.The p-value for this test is .0079.If the significance level set for the test is .01, we should

A)Reject the null hypothesis since $\alpha$ < p-value.
B)Reject the null hypothesis since t_stat > t_c
C)not Reject the null hypothesis since $\alpha$ > p-value
D)not Reject the null hypothesis since t_stat > t_c
E)Accept the null hypothesis since p-value < $\alpha$

Question 44

Type II error in hypothesis testing is

A)accepting a false null hypothesis
B)rejecting a true alternative hypothesis
C)rejecting a true null hypothesis
D)rejecting the sample result when it should have been accepted
E)none of the above

Question 45

A report stated that the average number of overtime hours for IRS workers during the past week was more than 10 hours per worker.You will test that statement with a sample of workers.What null and alternative hypotheses would you recommend here if you want to choose a null hypothesis that is skeptical of the report's number?

A) H₀: µ > 10 units (The average overtime is more than 10 hours.)
H_a: µ ≤ 10 units (The average overtime is no more than 10 hours.)
B) H₀: µ = 10 units (The average overtime is 10 hours.)
H_a: µ ≠ 10 units (The average overtime is not 10 hours.)
C) H₀: µ ≠ 10 units (The average overtime is not be 10 hours.)
H_a: µ = 10 units (The average overtime is 10 hours.)
D) H₀: µ ≤ 10 units (The average overtime is no more than 10 hours.)
H_a: µ > 10 units (The average overtime is more than 10 hours.)
E) H₀: µ < 10 units (The average overtime is less than 10 hours.)
H_a: µ > 10 units (The average overtime is more than 10 hours.)

Question 46

The competing hypotheses for a hypothesis test are as follows: H₀: The earth is flat.
H_a: The earth is round.
Describe what a Type I error and a Type II error would be here.

A)A Type I error here would be to believe the earth is the center of the solar system.A Type II error would be to believe that the earth is the only place in the universe where you can get a good hamburger.
B)A Type I error here would be to believe the earth is round when it's actually flat.A Type II error would be to believe that the earth is flat when it's actually round.
C)A Type I error here would be to believe the earth is flat when it's actually round.A Type II error would be to believe that the earth is round when it's actually flat.
D)A Type I error here would be to believe the earth revolves around the moon.A Type II error would be to believe that the sun revolves around the earth.
E)A Type I error here would be to believe the earth revolves around the sun.A Type II error would be to believe that the sun revolves around the earth.

Question 47

The average household size in the US in 2012 was 2.55 persons (Source: US Census Bureau).In order to test for a change in the average size of a household, the correct null and alternative hypothesis would be:

A) H₀: µ > 2.55 persons (The average household size is greater than 2.5 persons.)
H_a: µ ≤ 2.55 persons (The average household size is no more than 2.55 persons.)
B) H₀: µ = 2.55 persons (The average household size is 2.55 persons.)
H_a: µ ≠ 2.55 persons (The average household size is not 2.55 persons.)
C) H₀: µ ≠ 2.55 persons (The average household size is not 2.55 persons.)
H_a: µ = 2.55 persons (The average household size is 2.55 persons.)
D) H₀: µ ≤ 2.55 persons (The average household size is no more than 2.55 persons.)
H_a: µ > 2.55 persons (The average household size is greater than 2.55 persons.)
E) H₀: µ < 2.55 persons (The average household size is less than 2.55 persons.)
H_a: µ > 2.55 persons (The average household size is greater than 2.55 persons.)

Question 48

You are to test the following hypotheses: H₀: µ = 650
H_a: µ ≠ 650
A sample of size 20 produces a sample mean of 672, with a standard deviation of 42.The p-value for this two-tailed test is .0302.If the significance level set for the test is .05, we should

A)Reject the null hypothesis since $\alpha$ < p-value.
B)Reject the null hypothesis since p-value < $\alpha$ .
C)not Reject the null hypothesis since $\alpha$ > p-value
D)not Reject the null hypothesis since p-value > $\alpha$ .
E)Accept the null hypothesis since p-value < $\alpha$

Question 49

You are to test the following hypotheses: H₀: µ < 1500
H_a: µ > 1500
A sample of size 16 produces a sample mean of 1540, with a standard deviation of 100.The p-value for this test is .0652.If the significance level set for the test is .05, we should

A)Reject the null hypothesis since $\alpha$ < p-value.
B)Reject the null hypothesis since p-value < $\alpha$
C)not Reject the null hypothesis since $\alpha$ > p-value
D)not Reject the null hypothesis since p-value > $\alpha$
E)Accept the null hypothesis since $\alpha$ > p-value

Question 50

You are to test the following hypotheses: H₀: µ > 900
H_a: µ < 900
A sample of size 16 produces a sample mean of 882, with a standard deviation of 40.The p-value for this test is .0460.If the significance level set for the test is .01, we should

A)Reject the null hypothesis since $\alpha$ < p-value.
B)Reject the null hypothesis since p-value < $\alpha$ .
C)not Reject the null hypothesis since p-value > $\alpha$ .
D)not Reject the null hypothesis since $\alpha$ > p-value
E)Accept the null hypothesis since p-value < $\alpha$

Question 51

In recent years the average speed along a dangerous stretch of Highway 26 has been reported to be 55.8 mph.You plan to take a sample of cars along that stretch of highway to determine if the average speed recently is different from the reported average.What hypotheses would be appropriate for a hypothesis test here? Use a "status quo" approach to choose your null hypothesis.

A) H₀: µ = 55.8 mph
H_a: µ ≠ 55.8 mph
B) H₀: µ ≠ 55.8 mph
H_a: µ = 55.8 mph
C) H₀: µ > 55.8 mph
H_a: µ ≠ 55.8 mph
D) H₀: µ < 55.8 mph
H_a: µ = 55.8 mph
E) H₀: µ > 55.8 mph
H_a: µ = 55.8 mph

Question 52

You are to test the following hypotheses: H₀: µ < 940
H_a: µ > 940
A sample of size 49 produces a sample mean of 994, with a standard deviation of 130.The p-value for this test is

A).0036
B).0018
C).0009
D).0360

Question 53

In interval estimation, sample results are used to estimate the value of a population parameter.In hypothesis testing,

A)A hypothesis regarding a sample statistic is tested against the actual sample results.
B)A hypothesis regarding a population parameter is tested using sample results.
C)Sample results are used to form a hypothesis regarding a population.
D)The known values of population parameters are used to form a hypothesis about a sample statistic.
E)none of the above

Question 54

In 2011, adults who used text messaging on their cell phones sent and received an average of 41.5 texts per day (Source: PewInternet.org).You would like to determine whether there is evidence of an increase since 2011 in the average number of texts sent and received.Taking the "status quo" approach to form your null hypothesis, what would be the appropriate pair of hypotheses for your test?

A) H₀: µ > 41.5 texts (The average number of texts sent/received is greater than 41.5.)
H_a: µ ≤ 41.5 texts (The average number of texts sent/received is no more than 41.5.)
B) H₀: µ = 41.5 texts (The average number of texts sent/received is 41.5.)
H_a: µ ≠ 41.5 texts (The average number of texts sent/received is not 41.5.)
C) H₀: µ ≠ 41.5 texts (The average number of texts sent/received is not 41.5.)
H_a: µ = 41.5 texts (The average number of texts sent/received is 41.5 texts.)
D) H₀: µ ≤ 41.5 texts (The average number of texts sent/received is no more than 41.5.)
H_a: µ > 41.5 texts (The average number of texts sent/received is greater than 41.5.)
E) H₀: µ < 41.5 texts (The average number of texts sent/received is less than 41.5.)
H_a: µ > 41.5 texts (The average number of texts sent/received is greater than 41.5.)

Question 55

You are to test the following hypotheses: H₀: µ < 5500
H_a: µ > 5500
A sample of size 100 produces a sample mean of 5560, with a standard deviation of 420.The p-value for this test is

A).9234
B).1532
C).0383
D).0766

Question 56

Using the t distribution for a hypothesis test regarding a population mean is generally appropriate when

A)sample size is no more than 30
B)the sample standard deviation is being used
C)the population distribution is normal
D)a and b
E)a and c

Question 57

As sample size increases, and so degrees of freedom increase for a t distribution, the shape of the distribution.

A)becomes less skewed
B)is unaffected
C)looks more like a normal distribution
D)becomes bimodal
E)none of the above

Question 58

You are to test the following hypotheses: H₀: µ = 200
H_a: µ ≠ 200
A sample of size 25 produces a sample mean of 193, with a standard deviation of 28.The p-value for this two-tailed test is .2233.If the significance level set for the test is .10, we should

A)Reject the null hypothesis since $\alpha$ < p-value.
B)Reject the null hypothesis since p-value < $\alpha$ .
C)not Reject the null hypothesis since $\alpha$ > p-value
D)not Reject the null hypothesis since p-value > $\alpha$ .
E)Accept the null hypothesis since p-value < $\alpha$

Question 59

The fundamental hypothesis test in the American judicial system involves the following hypotheses: H₀: The accused is innocent.
H_a: The accused is guilty.
Describe what a Type I error and a Type II would involve here.

A)A Type I error would be to judge an innocent man guilty.A Type II error would be to judge a guilty man innocent.
B)A Type I error would be to judge a guilty man guilty.A Type II error would be to judge an innocent man innocent.
C)A Type I error would be to judge a guilty man innocent.A Type II error would be to judge an innocent man guilty.
D)A Type I error would be to judge an innocent man innocent.A Type II error would be to judge a guilty man guilty.
E)A Type I error would be to judge an innocent man guilty.A Type II error would be to judge a guilty man guilty.

Question 60

Type II error in hypothesis testing is

A)accepting the sample result when it should have been rejected
B)rejecting an alternative hypothesis that is actually true
C)accepting a null hypothesis when it is actually false
D)rejecting the sample result when it should have been accepted
E)none of the above

Question 61

You are to test the following hypotheses: H₀: µ = 40
H_a: µ ≠ 40
A sample of size 36 produces a sample mean of 42.2, with a standard deviation of 16.The p-value for this test is

A).0712
B).9288
C).4122
D).0265

Question 62

You are to test the following hypotheses: H₀: µ = 800
H_a: µ ≠ 800
A sample of size 81 produces a sample mean of 750, with a standard deviation of 216.The p-value for this test is

A).0186
B).0518
C).0372
D).0461