Question

The population mean for a Statistics test is 75 in a class that is usually taken by juniors and seniors. A random sample of 15 sophomores is selected from the course. The research question is whether or not sophomores are different from the average student in this class. The scores of the 15 sophomores are saved in a R variable “score". The R output is as follows:

> summary(score)
Min. 1st Qu. Median Mean 3rd Qu. Max. 49.0 61.0 71.0 67.6 74.5 84.0

> sd(score) [1] 10.64223

Given ? = 10.5 and using ? = 0.05, compute the sample size required to achieve a power

of 80% to reject the null when the true mean is 73.

f) Suppose in a different class, the assumptions were not adequate, so a bootstrap was done. Below are the results from 10,000 Bootstraps using the “score” data.

> quantile(scoreboot, probs = 0.05) 5%

63.06667
> quantile(scoreboot, probs = 0.95)

95% 71.86667

> quantile(scoreboot, probs = 0.025) 2.5%
62.2
> quantile(scoreboot, probs = 0.975) 97.5%

72.6
The researcher has changed his alternative to be ?!: ? < 75. Use the bootstrap results to answer that

hypothesis with a significance level ? = 0.05.

Answer 1

e)

power when true mean is 73

Using minitab

stat -> power and sample size -> 1-sample t

assuming alpha = 0.05 \

difference = 73- 75 = -2

power = 0.104272

f)

95th percentile is 71.86667 < 75

there is evidence that mean is less than 75

Please give me a thumbs-up if this helps you out. Thank you! :)