Hypothesis Test for a Population Mean (o is Unknown) You wish to test the following claim (Ha) at a significance level of a = 0.01. Ho:µ = 73.1 Ha:µ > 73.1 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 223 with mean M = 74 and a standard deviation of SD = 5.2. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) a greater than a This test statistic leads to a decision to... O reject the null accept the null fail to reject the null
Hypothesis Test for a Population Mean (o is Unknown) You wish to test the following claim (Ha) at a significance level of a = 0.01. Ho:µ = 73.1 Ha:µ > 73.1 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 223 with mean M = 74 and a standard deviation of SD = 5.2. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) a greater than a This test statistic leads to a decision to... O reject the null accept the null fail to reject the null
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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![**Hypothesis Test for a Population Mean (σ is Unknown)**
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.01\).
\[
H_0: \mu = 73.1 \\
H_a: \mu > 73.1
\]
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \(n = 223\) with mean \(M = 74\) and a standard deviation of \(SD = 5.2\).
**What is the test statistic for this sample?** (Report answer accurate to three decimal places.)
Test statistic = [ ]
**What is the p-value for this sample?** (Report answer accurate to four decimal places.)
p-value = [ ]
The p-value is…
- ○ less than (or equal to) \(\alpha\)
- ○ greater than \(\alpha\)
**This test statistic leads to a decision to…**
- ○ reject the null
- ○ accept the null
- ○ fail to reject the null
**As such, the final conclusion is that…**
- ○ There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 73.1.
- ○ There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 73.1.
- ○ The sample data support the claim that the population mean is greater than 73.1.
- ○ There is not sufficient sample evidence to support the claim that the population mean is greater than 73.1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b06cc1a-670c-4da3-86c8-aa55d4f56c06%2Fdca8881d-fab6-4700-b550-cf2e5729b622%2Fil08eo4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Test for a Population Mean (σ is Unknown)**
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.01\).
\[
H_0: \mu = 73.1 \\
H_a: \mu > 73.1
\]
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \(n = 223\) with mean \(M = 74\) and a standard deviation of \(SD = 5.2\).
**What is the test statistic for this sample?** (Report answer accurate to three decimal places.)
Test statistic = [ ]
**What is the p-value for this sample?** (Report answer accurate to four decimal places.)
p-value = [ ]
The p-value is…
- ○ less than (or equal to) \(\alpha\)
- ○ greater than \(\alpha\)
**This test statistic leads to a decision to…**
- ○ reject the null
- ○ accept the null
- ○ fail to reject the null
**As such, the final conclusion is that…**
- ○ There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 73.1.
- ○ There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 73.1.
- ○ The sample data support the claim that the population mean is greater than 73.1.
- ○ There is not sufficient sample evidence to support the claim that the population mean is greater than 73.1.
Expert Solution
Step 1
Given that :
Sample size (n) = 223
Mean (M) = 74
S. D. = 5.2
Here, we use z test of hypothesis.
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