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A Cilain or Pestaurants has historically had a mean wait time of 6 minutes for its customers. Recently, the restaurant added several very popular dishes back to their menu. Due to this, the manager suspects the wait time, µ, has increased. He takes a random sample of 38 customers. The mean wait time for the sample is 6.4 minutes. Assume the population standard deviation for the wait times is known to be 3.1 minutes. Can the manager conclude that the mean wait time is now greater than 6 minutes? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. H,: 0 O

A Cilain or Pestaurants has historically had a mean wait time of 6 minutes for its customers. Recently, the restaurant added several very popular dishes back to their menu. Due to this, the manager suspects the wait time, µ, has increased. He takes a random sample of 38 customers. The mean wait time for the sample is 6.4 minutes. Assume the population standard deviation for the wait times is known to be 3.1 minutes. Can the manager conclude that the mean wait time is now greater than 6 minutes? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. H,: 0 O

Calculus For The Life Sciences
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 Chalh of Pestaurants has historically had a mean wait time of 6 minutes for its customers. Recently, the restaurant added several very popular dishes back to their menu. Due to this, the manager suspects the wait time, µ, has increased. He takes a random sample of 38 customers. The mean wait time for the sample is 6.4 minutes. Assume the population standard deviation for the wait times is known to be 3.1 minutes. Can the manager conclude that the mean wait time is now greater than 6 minutes? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. ロ<ロ H: I 口EO 口=D (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"), Here is some other information to help you with your test. Zn 10 is the value that cuts off an area of 0.10 in the right tail. Z0.10 • The test statistic has a normal distribution and the value is given by z = Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed 03 O Two-tailed
Transcribed Image Text:A Chalh of Pestaurants has historically had a mean wait time of 6 minutes for its customers. Recently, the restaurant added several very popular dishes back to their menu. Due to this, the manager suspects the wait time, µ, has increased. He takes a random sample of 38 customers. The mean wait time for the sample is 6.4 minutes. Assume the population standard deviation for the wait times is known to be 3.1 minutes. Can the manager conclude that the mean wait time is now greater than 6 minutes? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. ロ<ロ H: I 口EO 口=D (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"), Here is some other information to help you with your test. Zn 10 is the value that cuts off an area of 0.10 in the right tail. Z0.10 • The test statistic has a normal distribution and the value is given by z = Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed 03 O Two-tailed
O Iwo-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places.) 02- Step 3: Enter the test statistic. (Round to 3 decimal places.) 0.1 -3 -2 -1 (c) Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the chain of restaurants. O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean wait time is now greater than 6 mninutes. Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean wait time is now greater than 6 minutes. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean wait time is now greater than 6 minutes. Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean wait time is now greater than 6 minutes.
Transcribed Image Text:O Iwo-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places.) 02- Step 3: Enter the test statistic. (Round to 3 decimal places.) 0.1 -3 -2 -1 (c) Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the chain of restaurants. O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean wait time is now greater than 6 mninutes. Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean wait time is now greater than 6 minutes. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to conclude that the mean wait time is now greater than 6 minutes. Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to conclude that the mean wait time is now greater than 6 minutes.
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