Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ, spent by customers at the supermarkets has been reported to be 35 minutes, but executives have good reason to believe that μ is greater than 35 minutes. The executives hire a statistical consultant and ask her to perform a statistical test. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 39 minutes and the standard deviation of the times to be 10 minutes. Based on this information, complete the parts below. (a) What are the null hypothesis Ho and the alternative hypothesis H, that should be used for the test? Ho :D H₁ :0 (b) Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making? (Choose one) (c) Suppose the true mean shopping time spent by customers at the supermarkets is 42 minutes. Fill in the blanks to describe a Type II error. A Type II error would be (Choose one) the hypothesis that μ is (Choose one) when, in fact, μ is (Choose one) (Choose one) ▼ μ 0<0 X X OSO 020 O=O S 0⁰ >O ?
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ, spent by customers at the supermarkets has been reported to be 35 minutes, but executives have good reason to believe that μ is greater than 35 minutes. The executives hire a statistical consultant and ask her to perform a statistical test. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 39 minutes and the standard deviation of the times to be 10 minutes. Based on this information, complete the parts below. (a) What are the null hypothesis Ho and the alternative hypothesis H, that should be used for the test? Ho :D H₁ :0 (b) Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making? (Choose one) (c) Suppose the true mean shopping time spent by customers at the supermarkets is 42 minutes. Fill in the blanks to describe a Type II error. A Type II error would be (Choose one) the hypothesis that μ is (Choose one) when, in fact, μ is (Choose one) (Choose one) ▼ μ 0<0 X X OSO 020 O=O S 0⁰ >O ?
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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![### Statistical Testing for Mean Shopping Time
**Scenario:**
Executives of a supermarket chain are interested in understanding the amount of time that customers spend in the stores during shopping trips. Historically, the mean shopping time, denoted by \(\mu\), spent by customers has been reported as 35 minutes. However, executives suspect that \(\mu\) is actually greater than 35 minutes. To investigate this claim, they hire a statistical consultant to perform a statistical test.
To conduct the test, the consultant collects a random sample of 5 shopping times at the supermarkets and finds the mean of these times to be 39 minutes, with a standard deviation of 10 minutes.
Based on this data, complete the following tasks:
---
**(a) Setting Up Hypotheses**
Identify the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\) to be tested.
\[
\begin{align*}
H_0 &: \, \mu = 35 \\
H_1 &: \, \mu > 35
\end{align*}
\]
---
**(b) Error Type**
Suppose the consultant decides not to reject the null hypothesis. What kind of error is she possibly making?
- Options: Type I error, Type II error, No error, Not enough information
---
**(c) Understanding Type II Error**
Suppose the true mean shopping time spent by customers at the supermarkets is actually 42 minutes. Fill in the blanks to describe a Type II error:
"A Type II error would be **failing to reject** the hypothesis that \(\mu\) is **equal to 35** when, in fact, \(\mu\) is **greater than 35**."
Options for filling the blanks:
1. Rejecting, Failing to reject
2. 35, 42
3. Equal to 35, Greater than 35, Less than 35
---
Analyzing the Results:
1. **Mean Calculation:** The mean (\(\overline{x}\)) of the sample is 39 minutes.
2. **Standard Deviation:** The standard deviation (\(s\)) is 10 minutes.
3. **Sample Size:** The sample size (\(n\)) is 5.
**Statistical Implications:**
The hypotheses setup clearly defines the expected average time and how the executive's presumption can be tested. Errors in hypothesis testing commonly include Type I error (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd1b6d45-a7eb-422c-8cfa-b963b51ff783%2F3c71fc01-9f9c-47ee-8e26-2657fc6d548e%2Fqt7lwqd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Testing for Mean Shopping Time
**Scenario:**
Executives of a supermarket chain are interested in understanding the amount of time that customers spend in the stores during shopping trips. Historically, the mean shopping time, denoted by \(\mu\), spent by customers has been reported as 35 minutes. However, executives suspect that \(\mu\) is actually greater than 35 minutes. To investigate this claim, they hire a statistical consultant to perform a statistical test.
To conduct the test, the consultant collects a random sample of 5 shopping times at the supermarkets and finds the mean of these times to be 39 minutes, with a standard deviation of 10 minutes.
Based on this data, complete the following tasks:
---
**(a) Setting Up Hypotheses**
Identify the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\) to be tested.
\[
\begin{align*}
H_0 &: \, \mu = 35 \\
H_1 &: \, \mu > 35
\end{align*}
\]
---
**(b) Error Type**
Suppose the consultant decides not to reject the null hypothesis. What kind of error is she possibly making?
- Options: Type I error, Type II error, No error, Not enough information
---
**(c) Understanding Type II Error**
Suppose the true mean shopping time spent by customers at the supermarkets is actually 42 minutes. Fill in the blanks to describe a Type II error:
"A Type II error would be **failing to reject** the hypothesis that \(\mu\) is **equal to 35** when, in fact, \(\mu\) is **greater than 35**."
Options for filling the blanks:
1. Rejecting, Failing to reject
2. 35, 42
3. Equal to 35, Greater than 35, Less than 35
---
Analyzing the Results:
1. **Mean Calculation:** The mean (\(\overline{x}\)) of the sample is 39 minutes.
2. **Standard Deviation:** The standard deviation (\(s\)) is 10 minutes.
3. **Sample Size:** The sample size (\(n\)) is 5.
**Statistical Implications:**
The hypotheses setup clearly defines the expected average time and how the executive's presumption can be tested. Errors in hypothesis testing commonly include Type I error (
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