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1:00 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. H.:µ = 56.3 Ha:µ < 56.3 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 6 with mean M = 43.4 and a standard deviation of SD = 12.6. 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... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is less than 56.3. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 56.3. O The sample data support the claim that the population mean is less than 56.3. There is not sufficient sample evidence to support the claim that the population mean is less than 56.3. A myopenmath.com - Private

1:00 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. H.:µ = 56.3 Ha:µ < 56.3 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 6 with mean M = 43.4 and a standard deviation of SD = 12.6. 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... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is less than 56.3. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 56.3. O The sample data support the claim that the population mean is less than 56.3. There is not sufficient sample evidence to support the claim that the population mean is less than 56.3. A myopenmath.com - Private

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 \(\alpha = 0.01\). \[ H_0: \mu = 56.3 \\ H_a: \mu < 56.3 \] You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \(n = 6\) with mean \(M = 43.4\) and a standard deviation of \(SD = 12.6\). **1. What is the test statistic for this sample?** (Report answer accurate to three decimal places.) - **Test statistic =** [ ] **2. What is the p-value for this sample?** (Report answer accurate to four decimal places.) - **p-value =** [ ] **3. The p-value is...** - [ ] less than (or equal to) \(\alpha\) - [ ] greater than \(\alpha\) **4. This test statistic leads to a decision to...** - [ ] reject the null - [ ] accept the null - [ ] fail to reject the null **5. As such, the final conclusion is that...** - [ ] There is sufficient evidence to warrant rejection of the claim that the population mean is less than 56.3. - [ ] There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 56.3. - [ ] The sample data support the claim that the population mean is less than 56.3. - [ ] There is not sufficient sample evidence to support the claim that the population mean is less than 56.3. --- This page provides a structured approach to conducting a hypothesis test for a population mean when the standard deviation is unknown. It guides you through calculating the test statistic, determining the p-value, and making a decision based on these calculations.
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 \(\alpha = 0.01\). \[ H_0: \mu = 56.3 \\ H_a: \mu < 56.3 \] You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \(n = 6\) with mean \(M = 43.4\) and a standard deviation of \(SD = 12.6\). **1. What is the test statistic for this sample?** (Report answer accurate to three decimal places.) - **Test statistic =** [ ] **2. What is the p-value for this sample?** (Report answer accurate to four decimal places.) - **p-value =** [ ] **3. The p-value is...** - [ ] less than (or equal to) \(\alpha\) - [ ] greater than \(\alpha\) **4. This test statistic leads to a decision to...** - [ ] reject the null - [ ] accept the null - [ ] fail to reject the null **5. As such, the final conclusion is that...** - [ ] There is sufficient evidence to warrant rejection of the claim that the population mean is less than 56.3. - [ ] There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 56.3. - [ ] The sample data support the claim that the population mean is less than 56.3. - [ ] There is not sufficient sample evidence to support the claim that the population mean is less than 56.3. --- This page provides a structured approach to conducting a hypothesis test for a population mean when the standard deviation is unknown. It guides you through calculating the test statistic, determining the p-value, and making a decision based on these calculations.
Expert Solution
Step 1

Given data:

Significance level = 0.01

n = 6

M = 43.4

S.d = 12.6

steps

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