Given the sample mean = 21.325, sample standard deviation = 5.5856, and N = 40 for the low income group, Test the claim that the mean nickel diameter drawn by children in the low income group is greater than 21.21 mm. Test at the 0.1 significance level. a) Identify the correct alternative hypothesis: Ομ< 21.21

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**Statistical Hypothesis Testing: Nickel Diameter in Low Income Group**

**Given Data:**
- Sample Mean (\(\bar{x}\)) = 21.325 mm
- Sample Standard Deviation (s) = 5.5856 mm
- Sample Size (N) = 40

**Research Claim:**
Test the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm. Conduct the test at a 0.1 significance level.

**a) Identify the Correct Alternative Hypothesis:**
Select the appropriate alternative hypothesis:

- \( \mu < 21.21 \)
- \( p > 21.21 \)
- \( p < 21.21 \)
- \( \mu > 21.21 \)  [Correct choice for this scenario]
- \( \mu = 21.21 \)
- \( p = 21.21 \)

**Instructions:**
All answers should be rounded to three decimal places.

**b) Calculate the Test Statistic:**
Enter the test statistic value: [___]

**c) Determine the Critical Value:**
Using the Traditional method, find the critical value: [___]

**d) Decision Based on Hypothesis Test:**
Decide whether to:

- Reject \( H_0 \)
- Fail to reject \( H_0 \) 

This process enables statistical conclusions on whether the mean diameter exceeds the specified value, using hypothesis testing techniques appropriate for the given sample data.
Transcribed Image Text:**Statistical Hypothesis Testing: Nickel Diameter in Low Income Group** **Given Data:** - Sample Mean (\(\bar{x}\)) = 21.325 mm - Sample Standard Deviation (s) = 5.5856 mm - Sample Size (N) = 40 **Research Claim:** Test the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm. Conduct the test at a 0.1 significance level. **a) Identify the Correct Alternative Hypothesis:** Select the appropriate alternative hypothesis: - \( \mu < 21.21 \) - \( p > 21.21 \) - \( p < 21.21 \) - \( \mu > 21.21 \) [Correct choice for this scenario] - \( \mu = 21.21 \) - \( p = 21.21 \) **Instructions:** All answers should be rounded to three decimal places. **b) Calculate the Test Statistic:** Enter the test statistic value: [___] **c) Determine the Critical Value:** Using the Traditional method, find the critical value: [___] **d) Decision Based on Hypothesis Test:** Decide whether to: - Reject \( H_0 \) - Fail to reject \( H_0 \) This process enables statistical conclusions on whether the mean diameter exceeds the specified value, using hypothesis testing techniques appropriate for the given sample data.
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