Question 1

$\alpha = 0.08 , \mathrm { p } \text {-value } = 0.10$
A) Fail to reject $\mathrm { H } _ { 0 }$
B) Reject $\mathrm { H } _ { 0 }$

Accepted Answer

The answer of \(\alpha = 0.08 , \mathrm { p...

Question 2

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Find the large-sample rejection region for the test of interest to the college when using a level of significance of 0.05. A) Reject H0 if z < -1.645 or z > 1.645. B) Reject H0 if z < -1.96 or z > 1.96. C) Reject H0 if z > 1.645. D) Reject H0 if z < -1.96.

Accepted Answer

The rejection region for a two-tailed test at a 0.05 significance level is z < -1.96 or z > 1.96.

Question 3

A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the weight of the chicken. The store advertises that the average weight of their chickens is 4.6 pounds. A random sample of 30 of the store's chickens yielded the weights (in pounds) shown below. $$\begin{array} { l l l l l l l l l l } 
4.4 & 4.7 & 4.6 & 4.4 & 4.5 & 4.3 & 4.6 & 4.5 & 4.6 & 4.9 \
4.6 & 4.8 & 4.3 & 4.4 & 4.7 & 4.5 & 4.2 & 4.3 & 4.1 & 4.0 \
4.5 & 4.6 & 4.2 & 4.4 & 4.7 & 4.8 & 5.0 & 4.2 & 4.1 & 4.5
\end{array}$$ Test whether the population mean weight of the chickens is less than 4.6 pounds. Use α = .05.

Accepted Answer

The answer of A supermarket sells rotisserie chicken at a...

Question 4

The scores on a standardized test are reported by the testing agency to have a mean of 70. Based on his personal observations, a school guidance counselor believes the mean score is much higher. He collects the following scores from a sample of 50 randomly chosen students who took the test. $$\begin{array} { l l l l l l l l l l } 
39 & 48 & 55 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \
71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \
79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \
85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \
90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 99
\end{array}$$ Use the data to conduct a test of hypotheses at α = .05 to determine whether there is any evidence to support the counselor's suspicions.

Accepted Answer

The answer of The scores on a standardized test are...

Question 5

A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of n = 200 cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. Find the large-sample rejection region appropriate for this test if we are using α = 0.05. A) Reject $\mathrm { H } _ { 0 }$ if $\mathrm { z } < - 1.645$ or $\mathrm { z } > 1.645$. B) Reject $\mathrm { H } _ { 0 }$ if $\mathrm { z } < - 1.96$ or $\mathrm { z } > 1.96$. C) Reject $\mathrm { H } _ { 0 }$ if $\mathrm { z } > 1.645$. D) Reject $\mathrm { H } _ { 0 }$ if $\mathrm { z } < - 1.96$.

Accepted Answer

The answer of A consumer product magazine recently ran a...

Question 6

Consider a test of H0: μ = 30 performed with the computer. SPSS reports a two-tailed p-value of 0.0164. Make the appropriate conclusion for the given situation: Ha: μ > 30, z = -2.4, α = 0.01
A) Fail to reject H0
B) Reject H0

Accepted Answer

The p-value for a one-tailed test (Ha: μ > 30) would be half of the two-tailed p-value, which is 0.0082. However, since the z-value is negative (-2.4), it indicates that the sample mean is less than 30, not greater. Therefore, we fail to reject H0.

Question 7

Given $H _ { 0 } : \mu = 25 , H _ { \mathrm { a } } : \mu \neq 25$, and $p = 0.034$. Do you reject or fail to reject $H _ { 0 }$ at the $.01$ level of significance?
A) fail to reject $H _ { 0 }$
B) reject $\mathrm { H } _ { 0 }$
C) not sufficient information to decide

Accepted Answer

The answer of Given \(H _ { 0 } :...

Question 8

Suppose we wish to test $H _ { 0 } : \mu = 23$ vs. $H _ { \mathrm { a } } : \mu < 23$. Which of the following possible sample restults gives the most evidence to support $H _ { a }$ (i.e., reject $H _ { 0 }$ )?
A) $\bar { x } = 19 , s = 5$
B) $\bar { x } = 20 , s = 8$
C) $\bar { x } = 21 , s = 6$
D) $\bar { x } = 19 , s = 11$

Accepted Answer

The answer of Suppose we wish to test \(H _...

Question 9

A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 67 hours. In order to test whether the time to fill out the form has been reduced, a sample of 81 small business owners who annually complete the form was randomly chosen and their completion times recorded. The mean completion time for the sample was 66.7 hours with a standard deviation of 15 hours. State the rejection region for the desired test at α = .10.

Accepted Answer

The answer of A revenue department is under orders to...

Question 10

$\alpha = 0.08 , \mathrm { p } \text {-value } = 0.001$
A) Reject $\mathrm { H } _ { 0 }$
B) Fail to reject $\mathrm { H } _ { 0 }$

Accepted Answer

The answer of \(\alpha = 0.08 , \mathrm { p...

Question 11

Consider a test of H0: μ = 65 performed with the computer. SPSS reports a two-tailed p-value of 0.0892. Make the appropriate conclusion for the given situation: Ha: μ < 65, z = -1.7, α = 0.05
A) Reject H0
B) Fail to reject H0

Accepted Answer

The answer of Consider a test of H0: μ =...

Question 12

State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 940 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 940 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the .01 significance level. Suppose 99 bulbs were tested with the following results: $\bar { x }$ = 962 hours, s = 77 hours. Find the rejection region for the test of interest to the State University.

Accepted Answer

The answer of State University uses thousands of fluorescent light...

Question 13

How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 69 tissues during a cold. Suppose a random sample of 2500 people yielded the following data on the number of tissues used during a cold: $\bar { x } = 60 , s = 16$. Suppose the corresponding test statistic falls in the rejection region at $\alpha = , 05$. What is the correct conclusion?
A) At $\alpha = .05$, reject $H _ { 0 }$.
B) At $\alpha = .10$, reject $H _ { 0 }$.
C) At $\alpha = .05$, accept $H _ { a }$.
D) At $\alpha = .10$, reject $H _ { a }$.

Accepted Answer

The answer of How many tissues should a package of...

Question 14

State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 800 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 800 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the .05 significance level. Suppose 121 bulbs were tested with the following results: $\bar { x }$ = 827.5 hours, s = 110 hours. Conduct the test using α = .05.

Accepted Answer

The answer of State University uses thousands of fluorescent light...

Question 15

Consider a test of $\mathrm { H } _ { 0 } : \mu = 80$ performed with the computer. SPSS reports a two-tailed p-value of $0.0038$. Make the appropriate conclusion for the given situation: $\mathrm { H } _ { \mathrm { a } } : \mu \neq 80 , z = 2.9 , \alpha = 0.04$
A) Reject $\mathrm { H } _ { 0 }$
B) Fail to reject $\mathrm { H } _ { 0 }$

Accepted Answer

The answer of Consider a test of \(\mathrm { H...

Question 16

We have created a $99 \%$ confidence interval for $\mu$ with the result $( 10,15 )$. What conclusion will we make if we test $H _ { 0 } : \mu = 17$ vs. $H _ { \mathrm { a } } : \mu \neq 17$ at $\alpha = .01$ ?
A) Reject $\mathrm { H } _ { 0 }$ in favor of $H _ { a }$.
B) Accept $\mathrm { H } _ { 0 }$ rather than $\mathrm { H } _ { \mathrm { a } }$ -
C) Fail to reject $\mathrm { H } _ { 0 }$.
D) We cannot tell what our decision will be with the information given.

Accepted Answer

The answer of We have created a $99 \%$ confidence...

Question 17

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Suppose the sample mean and sample standard deviation were calculated to be 23.2 and 20.26 minutes, respectively. Calculate the value of the test statistic to be used in the test.
A) z = 2.437
B) z = 37.59
C) z = 0.173
D) z = 2.551

Accepted Answer

The test statistic for a hypothesis test about a population mean is given by:z = (x̄ - μ) / (σ / √n)where x̄ is the sample mean, μ is the hypothesized population mean, σ is the population standard deviation, and n is the sample size.In this case, we have x̄ = 23.2, μ = 20, σ = 20.26, and n = 238. Plugging these values into the formula, we get:z = (23.2 - 20) / (20.26 / √238) = 2.437Therefore, the value of the test statistic is 2.437.

Question 18

A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 16 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of n = 50 wind speed recordings (taken at random intervals), the wind speed at the site averaged x = 16.7 mph, with a standard deviation of s = 3.6 mph. To determine whether the site meets the organization's requirements, consider the test, H0: μ = 16 vs. Ha: μ > 16, where μ is the true mean wind speed at the site and α = .01. Suppose the value of the test statistic were computed to be 1.37. State the conclusion.
A) At α = .01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 16 mph.
B) At α = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 16 mph.
C) We are 99% confident that the site meets the organization's requirements.
D) We are 99% confident that the site does not meet the organization's requirements.

Accepted Answer

The test statistic of 1.37 is less than the critical value for α = .01 in a one-tailed test, which is approximately 2.33. Therefore, we fail to reject the null hypothesis, indicating insufficient evidence to conclude that the true mean wind speed exceeds 16 mph.

Question 19

Consider a test of H0: μ = 70 performed with the computer. SPSS reports a two-tailed p-value of 0.2302. Make the appropriate conclusion for the given situation: Ha: μ > 70, z = 1.20, α = 0.10
A) Fail to reject H0
B) Reject H0

Accepted Answer

The p-value for a one-tailed test (Ha: μ > 70) is half of the two-tailed p-value, which is 0.1151. Since 0.1151 > α = 0.10, we fail to reject H0.

Question 20

Given $H _ { 0 } : \mu = 18 , H _ { \mathrm { a } } : \mu < 18$, and $p = 0.068$. Do you reject or fail to reject $H _ { 0 }$ at the $.05$ level of significance?
A) fail to reject $H _ { 0 }$
B) reject $H _ { 0 }$
C) not sufficient information to decide

Accepted Answer

The answer of Given \(H _ { 0 } :...

Quiz 8: Inferences Based on a Single Sample: Tests of Hypothesis

$\alpha = 0.08 , \mathrm { p } \text {-value } = 0.10$ A) Fail to reject $\mathrm { H } _ { 0 }$ B) Reject $\mathrm { H } _ { 0 }$

Consider a test of H0: μ = 30 performed with the computer. SPSS reports a two-tailed p-value of 0.0164. Make the appropriate conclusion for the given situation: Ha: μ > 30, z = -2.4, α = 0.01

Given $H _ { 0 } : \mu = 25 , H _ { \mathrm { a } } : \mu \neq 25$ , and $p = 0.034$ . Do you reject or fail to reject $H _ { 0 }$ at the $.01$ level of significance? A) fail to reject $H _ { 0 }$ B) reject $\mathrm { H } _ { 0 }$ C) not sufficient information to decide

$\alpha = 0.08 , \mathrm { p } \text {-value } = 0.001$ A) Reject $\mathrm { H } _ { 0 }$ B) Fail to reject $\mathrm { H } _ { 0 }$

Consider a test of H0: μ = 65 performed with the computer. SPSS reports a two-tailed p-value of 0.0892. Make the appropriate conclusion for the given situation: Ha: μ < 65, z = -1.7, α = 0.05

Consider a test of H0: μ = 70 performed with the computer. SPSS reports a two-tailed p-value of 0.2302. Make the appropriate conclusion for the given situation: Ha: μ > 70, z = 1.20, α = 0.10

Given $H _ { 0 } : \mu = 18 , H _ { \mathrm { a } } : \mu < 18$ , and $p = 0.068$ . Do you reject or fail to reject $H _ { 0 }$ at the $.05$ level of significance? A) fail to reject $H _ { 0 }$ B) reject $H _ { 0 }$ C) not sufficient information to decide