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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
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.
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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