MATLAB: An Introduction with Applications
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Author: Amos Gilat
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![**Hypothesis Test for a Population Mean (\(\sigma\) is Known)**
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.05\).
- \(H_0: \mu = 53.7\)
- \(H_a: \mu > 53.7\)
You believe the population is normally distributed and you know the population standard deviation is \(\sigma = 10.1\). You obtain a sample mean of \(M = 57.5\) for a sample of size \(n = 63\).
**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 three 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 hypothesis
- ( ) accept the null hypothesis
- ( ) fail to reject the null hypothesis
As such, the final conclusion is that...
- ( ) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 53.7.
- ( ) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 53.7.
- ( ) The sample data support the claim that the population mean is greater than 53.7.
- ( ) There is not sufficient sample evidence to support the claim that the population mean is greater than 53.7.](https://content.bartleby.com/qna-images/question/5b06cc1a-670c-4da3-86c8-aa55d4f56c06/5d8dc734-9ec0-409a-b2a8-ec03a787b9f1/xlvjhag_processed.jpeg)
Transcribed Image Text:**Hypothesis Test for a Population Mean (\(\sigma\) is Known)**
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.05\).
- \(H_0: \mu = 53.7\)
- \(H_a: \mu > 53.7\)
You believe the population is normally distributed and you know the population standard deviation is \(\sigma = 10.1\). You obtain a sample mean of \(M = 57.5\) for a sample of size \(n = 63\).
**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 three 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 hypothesis
- ( ) accept the null hypothesis
- ( ) fail to reject the null hypothesis
As such, the final conclusion is that...
- ( ) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 53.7.
- ( ) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 53.7.
- ( ) The sample data support the claim that the population mean is greater than 53.7.
- ( ) There is not sufficient sample evidence to support the claim that the population mean is greater than 53.7.
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