A very large company is interested in its employees' productivity. The company reports from its historical data that its employees spend a mean of 164 minutes per employee (on a typical day) dealing with email. To test this claim, an independent consultant chooses 26 employees at random and finds that those employees spend a sample mean of 172 minutes dealing with email, with a sample standard deviation of 21 minutes. Assume that the population of amounts of time employees spend dealing with email is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to reject the claim that 4, the mean number of minutes employees spend dealing with email, is equal to 164. (a) State the null hypothesis Ho and the alternative hypothesis H1 that you would use for the test.
A very large company is interested in its employees' productivity. The company reports from its historical data that its employees spend a mean of 164 minutes per employee (on a typical day) dealing with email. To test this claim, an independent consultant chooses 26 employees at random and finds that those employees spend a sample mean of 172 minutes dealing with email, with a sample standard deviation of 21 minutes. Assume that the population of amounts of time employees spend dealing with email is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to reject the claim that 4, the mean number of minutes employees spend dealing with email, is equal to 164. (a) State the null hypothesis Ho and the alternative hypothesis H1 that you would use for the test.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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![A very large company is interested in its employees' productivity. The company reports from its historical data that its employees spend a mean
of 164 minutes per employee (on a typical day) dealing with email. To test this claim, an independent consultant chooses 26 employees at
random and finds that those employees spend a sample mean of 172 minutes dealing with email, with a sample standard deviation of 21
minutes. Assume that the population of amounts of time employees spend dealing with email is approximately normally distributed.
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to reject the claim
that u, the mean number of minutes employees spend dealing with email, is equal to 164.
(a) State the null hypothesis H, and the alternative hypothesis H1 that you would use for the test.
Họ: 0
H: 0
OSO
O=0
?
(b) Perform a t test and find the p-value.
Here is some information to help you with your i test.
The value of the test statistic is given by t =
The p-value is two times the area under the curve to the right of the value of the test statistic.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84510c0d-50c4-4f29-b3b9-b60c8e3696bd%2Fb3ae4ace-8c0e-49f3-9643-a7044a5e38ba%2Fllf00g9_processed.png&w=3840&q=75)
Transcribed Image Text:A very large company is interested in its employees' productivity. The company reports from its historical data that its employees spend a mean
of 164 minutes per employee (on a typical day) dealing with email. To test this claim, an independent consultant chooses 26 employees at
random and finds that those employees spend a sample mean of 172 minutes dealing with email, with a sample standard deviation of 21
minutes. Assume that the population of amounts of time employees spend dealing with email is approximately normally distributed.
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to reject the claim
that u, the mean number of minutes employees spend dealing with email, is equal to 164.
(a) State the null hypothesis H, and the alternative hypothesis H1 that you would use for the test.
Họ: 0
H: 0
OSO
O=0
?
(b) Perform a t test and find the p-value.
Here is some information to help you with your i test.
The value of the test statistic is given by t =
The p-value is two times the area under the curve to the right of the value of the test statistic.
![Student's t Distribution
Step 1: Enter the number of degrees
af freedom.
Step 2: Select ae-lailed or twa-tailed.
O Oe-taled
O Tmo tailed
Step 3: Enter the test statistic.
(Round to 3 decimal places.)
Step 4: Shade the area represanted by
the p-value.
Step 5: Enter the p-value.
(Round to 3 decimal places.)
(c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the company.
O since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is
enough evidence to reject the claim that the mean number of minutes employees spend dealing with email is equal to
164.
O since the p-value is less than (or equal to) the level of significance, the null hypothesis is nat rejected. So, there is
not enough evidence to reject the claim that the mean number of minutes employees spend dealing with email is
equal to 164.
O since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough
evidence to reject the claim that the mean number of minutes employees spend dealing with email is equal to 164.
O since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough
evidence to reject the claim that the mean number of minutes employees spend dealing with email is equal to 164.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84510c0d-50c4-4f29-b3b9-b60c8e3696bd%2Fb3ae4ace-8c0e-49f3-9643-a7044a5e38ba%2Fvp6y4zi_processed.png&w=3840&q=75)
Transcribed Image Text:Student's t Distribution
Step 1: Enter the number of degrees
af freedom.
Step 2: Select ae-lailed or twa-tailed.
O Oe-taled
O Tmo tailed
Step 3: Enter the test statistic.
(Round to 3 decimal places.)
Step 4: Shade the area represanted by
the p-value.
Step 5: Enter the p-value.
(Round to 3 decimal places.)
(c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the company.
O since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is
enough evidence to reject the claim that the mean number of minutes employees spend dealing with email is equal to
164.
O since the p-value is less than (or equal to) the level of significance, the null hypothesis is nat rejected. So, there is
not enough evidence to reject the claim that the mean number of minutes employees spend dealing with email is
equal to 164.
O since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough
evidence to reject the claim that the mean number of minutes employees spend dealing with email is equal to 164.
O since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough
evidence to reject the claim that the mean number of minutes employees spend dealing with email is equal to 164.
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