Tom has recently designed a new escape room for a particular recreational centre. Before Tom launches the escape room for paying customers, he would like to get a better idea of how long it would typically take a group of people to solve the escape room. The escape room is designed to be completed by five to six people and will have a time limit of 120 minutes. Tom thinks that the escape room is actually much easier when there are five people in the group than when there are six people in the group. Tom wants to test the claim that the mean time it takes a group with five people to complete the escape room is less than the mean time it takes a group with six people to complete the escape room. To do this, Tom will perform a two-sample t-test for population mean. Let μ5 be the true mean time it takes a group of five people to complete the escape room and let µ6 be the true mean time it takes a group of six people to complete the escape room. Then Tom wants to test H₁ : μ5 - µ6 ≥ 0 versus Ha : µ5 – µ6 < 0. Tom invites 24 different groups of five people to try and solve the escape room and records how long it takes each of them to escape. Among these 24 groups, the average time it took them to escape is 114.8 minutes with a standard deviation of 4 minutes. Tom also invites 24 different groups of six people to solve the escape room and records how long it took each of them to escape. Among these 24 groups, the average time it took them to escape is 116.9 minutes with a standard deviation of 9.8 minutes. Note that Tom does not set a time limit and allows each group to take however long is needed. a) Compute the observed value of the test statistic. (Enter your answer correct to at least four decimal places)
Tom has recently designed a new escape room for a particular recreational centre. Before Tom launches the escape room for paying customers, he would like to get a better idea of how long it would typically take a group of people to solve the escape room. The escape room is designed to be completed by five to six people and will have a time limit of 120 minutes. Tom thinks that the escape room is actually much easier when there are five people in the group than when there are six people in the group. Tom wants to test the claim that the mean time it takes a group with five people to complete the escape room is less than the mean time it takes a group with six people to complete the escape room. To do this, Tom will perform a two-sample t-test for population mean. Let μ5 be the true mean time it takes a group of five people to complete the escape room and let µ6 be the true mean time it takes a group of six people to complete the escape room. Then Tom wants to test H₁ : μ5 - µ6 ≥ 0 versus Ha : µ5 – µ6 < 0. Tom invites 24 different groups of five people to try and solve the escape room and records how long it takes each of them to escape. Among these 24 groups, the average time it took them to escape is 114.8 minutes with a standard deviation of 4 minutes. Tom also invites 24 different groups of six people to solve the escape room and records how long it took each of them to escape. Among these 24 groups, the average time it took them to escape is 116.9 minutes with a standard deviation of 9.8 minutes. Note that Tom does not set a time limit and allows each group to take however long is needed. a) Compute the observed value of the test statistic. (Enter your answer correct to at least four decimal places)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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By the way, Can you calculate the p value for the question. Thank you.
Transcribed Image Text:Tom has recently designed a new escape room for a particular recreational centre. Before Tom launches the escape
room for paying customers, he would like to get a better idea of how long it would typically take a group of people to
solve the escape room. The escape room is designed to be completed by five to six people and will have a time limit
of 120 minutes.
Tom thinks that the escape room is actually much easier when there are five people in the group than when there are
six people in the group. Tom wants to test the claim that the mean time it takes a group with five people to complete
the escape room is less than the mean time it takes a group with six people to complete the escape room. To do this,
Tom will perform a two-sample t-test for population mean.
Let μ5 be the true mean time it takes a group of five people to complete the escape room and let μ6 be the true
mean time it takes a group of six people to complete the escape room. Then Tom wants to test
Ho: M5-M60 versus Ha: μ5 - µ6 <0.
Tom invites 24 different groups of five people to try and solve the escape room and records how long it takes each of
them to escape. Among these 24 groups, the average time it took them to escape is 114.8 minutes with a standard
deviation of 4 minutes. Tom also invites 24 different groups of six people to solve the escape room and records how
long it took each of them to escape. Among these 24 groups, the average time it took them to escape is
116.9 minutes with a standard deviation of 9.8 minutes. Note that Tom does not set a time limit and allows each
group to take however long is needed.
a) Compute the observed value of the test statistic.
(Enter your answer correct to at least four decimal places)
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