You wish to test the following claim (Ha) at a significance level of a = 0.001. H.:µ = 67.5 Ha: µ + 67.5 You believe the population is normally distributed and you know the standard deviation is o = 18.9 . You obtain a sample mean of M 72.2 for a sample of size n = 46. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = | 1.687 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 O greater than a
You wish to test the following claim (Ha) at a significance level of a = 0.001. H.:µ = 67.5 Ha: µ + 67.5 You believe the population is normally distributed and you know the standard deviation is o = 18.9 . You obtain a sample mean of M 72.2 for a sample of size n = 46. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = | 1.687 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 O greater than a
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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What is the p-value for this sample? ( Report answer accurate to four decimal places.)
p-value=

Transcribed Image Text:**Hypothesis Testing Overview**
In this example, we are testing a hypothesis about a population mean (\( \mu \)) at a significance level (\( \alpha \)) of 0.001.
**Null and Alternative Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( \mu = 67.5 \)
- Alternative Hypothesis (\( H_a \)): \( \mu \neq 67.5 \)
**Population and Sample Details:**
- The population is assumed to be normally distributed.
- Known standard deviation (\( \sigma \)): 18.9
- Sample mean (\( M \)): 72.2
- Sample size (\( n \)): 46
**Statistical Analysis:**
1. **Test Statistic Calculation:**
- The test statistic calculated for this sample is 1.687. This value is reported to three decimal places.
2. **P-Value for the Sample:**
- The p-value is to be calculated and reported to four decimal places.
3. **Conclusion about P-Value:**
- Based on the provided options, the p-value is greater than \( \alpha \).
This educational example illustrates how to conduct a hypothesis test with a known standard deviation, calculate the test statistic, and interpret the p-value in the context of the significance level.
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