Question 1: Hypothesis Testing. The regional manager at Coffbucks claims that the average customer spends 35 AED per visit. What the manager doesn't know that you are an undercover, international auditor for Coffbucks HQ. You aren't sure whether the true average is higher or lower, but you want to test to see if the manager is right or wrong. You observe transactions at several randomly selected branches and can safely assume that transactions are normally distributed. You observe x= 31, s² = 117, n₁ = 130 (a) Construct a 95% confidence interval around the estimate. Do you have sufficient evidence to reject the manager's claim? (b) You're interested in seeing how Coffbucks compares to its largest competitor, Coffsta, so you collect data on Coffsta sales too. You observe y = 26, s²y = 140, n2 = 95. Construct a 95% confidence interval for x-y. Do you have evidence that average sales at Coffbucks are significantly higher than those at Coffsta? How do you know? (c) You believe that Coffbucks sales at branches located in malls will be different from sales at branches not located in malls. To test this, you collect data from 152 branches and estimate the Simple Linear Regression sales = Bo + B₁mall + u, where sales are average sales and mall is a dummy variable coded 1 if the branch is in a mall and 0 if the branch is not in a mall. You observe P₁= 3.5, with standard error s.e. = 1.3. Execute a t-test to evaluate your claim (use the 95% level of confidence).
Question 1: Hypothesis Testing. The regional manager at Coffbucks claims that the average customer spends 35 AED per visit. What the manager doesn't know that you are an undercover, international auditor for Coffbucks HQ. You aren't sure whether the true average is higher or lower, but you want to test to see if the manager is right or wrong. You observe transactions at several randomly selected branches and can safely assume that transactions are normally distributed. You observe x= 31, s² = 117, n₁ = 130 (a) Construct a 95% confidence interval around the estimate. Do you have sufficient evidence to reject the manager's claim? (b) You're interested in seeing how Coffbucks compares to its largest competitor, Coffsta, so you collect data on Coffsta sales too. You observe y = 26, s²y = 140, n2 = 95. Construct a 95% confidence interval for x-y. Do you have evidence that average sales at Coffbucks are significantly higher than those at Coffsta? How do you know? (c) You believe that Coffbucks sales at branches located in malls will be different from sales at branches not located in malls. To test this, you collect data from 152 branches and estimate the Simple Linear Regression sales = Bo + B₁mall + u, where sales are average sales and mall is a dummy variable coded 1 if the branch is in a mall and 0 if the branch is not in a mall. You observe P₁= 3.5, with standard error s.e. = 1.3. Execute a t-test to evaluate your claim (use the 95% level of confidence).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:Question 1: Hypothesis Testing.
The regional manager at Coffbucks claims that the average customer spends 35
AED per visit. What the manager doesn't know is that you are an undercover,
international auditor for Coffbucks HQ. You aren't sure whether the true average
is higher or lower, but you want to test to see if the manager is right or wrong. You
observe transactions at several randomly selected branches and can safely assume
that transactions are normally distributed. You observe x= 31,
s² = 117, n₁ = 130
(a) Construct a 95% confidence interval around the estimate. Do you have
sufficient evidence to reject the manager's claim?
(b) You're interested in seeing how Coffbucks compares to its largest
competitor, Coffsta, so you collect data on Coffsta sales too. You observe y = 26,
s²y = 140, n2 = 95. Construct a 95% confidence interval for x-y. Do you have
evidence that average sales at Coffbucks are significantly higher than those at
Coffsta? How do you know?
(c) You believe that Coffbucks sales at branches located in malls will be
different from sales at branches not located in malls. To test this, you collect data
from 152 branches and estimate the Simple Linear Regression sales - Bo + Bimall
+ u, where sales are average sales and mall is a dummy variable coded 1 if the
branch is in a mall and 0 if the branch is not in a mall. You observe P₁ = 3.5, with
standard error s.e. = 1.3. Execute a t-test to evaluate your claim (use the 95% level
of confidence).
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