Question

5) Construct a complete hypothesis test and determine if the two groups (population mean vs sample mean) have significantly different balance using Alpha Level -> a=0.05. The Hypothesis Test should include: 1. Null and Alternative Hypothesis 2. Standard Error of the Mean 3. Standard Score Zoo 4. Alpha Level –Critical Zcore (two-tail test) 5. Conclusion: a. fail to reject H, or b. reject H, 6. Conclusion with reference to original hypothesis statement “if if the two groups (population mean vs sample mean) have significantly different balance times"

Answer 1

1. Null and alternative Hypothesis:

$H_{0}:\mu=108.6$

$H_{1}:\mu\ne108.6$

2. Standard error of the mean is given by : $SE=\frac{\sigma}{\sqrt{n}}=\frac{35.85945}{\sqrt{10}}=\frac{35.85945}{3.1623}=11.3398$

3. Z score: $Z=\frac{\bar{X}-\mu}{SE}=\frac{101-108.6}{11.3398}=-0.6702$

4.Alpha level Critical Z-score=1.96

5.Conclusion: a. Fail to reject

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6. Since we fail to reject the Null Hypothesis, we conclude that there is no sufficient evidence in the claim that the two groups (population mean and the sample mean) have different balance times.