Question

Show work please.

Compute z-scores or t-scores accordingly then find their one-tailed AND two-tailed p-value the following situations. Then, summarize the results of the analysis at α level 0.05.

The mean BMI of US men is 26 with the population standard deviation of 4. You have data from a sample of 25 US men with type II diabetes, who are attending a diabetes health promotion program. The mean BMI of the sample is 28.34.

Answer 1

Given that, population mean (μ) = 26 and

population standard deviation = 4

Sample size (n) = 25 and sample mean = 28.34

Since, population standard deviation is known we used z-test.

Test statistic is,

=> Test statistic = Z = 2.93

For One-tailed :

p-value = P(Z > 2.93) = 1 - P(Z < 2.93) = 1 - 0.9983 = 0.0017

=> p-value = 0.0017

For two-tailed test :

p-value = 2 * P(Z > 2.93) = 2 * 0.0017 = 0.0034

=> p-value = 0.0034