A researcher asks whether attending a private high school leads to higher or lower performance on a test of social skills when compared to students attending public schools. A sample of 100 students from a private school produces a mean score of 71.30. The population mean (m) for students from public high schools is 75.62. The population standard deviation is 28. Zobt is –1.54. Zcrit is ± 1.96.

Question

Should the researcher use a one-tailed or a two-tailed test? Why?
What is the alternative hypothesis?
What is the null hypothesis?
What should the researcher conclude about this relationship in the population?
Are the results significant? Explain your response.
What is the probability of making a Type I error?
If a Type I error were made, what would it mean?
What is the probability of making a Type II error?
If a Type II error were made, what would it mean?

Answer 1

We do not do your work for you. Once you have attempted to answer your questions, we will be happy to give you feedback on your work. Although it might require more time and effort, you will learn more if you do your own work. Isn't that why you go to school?

However, I will give you a start.

If you are considering both higher or lower, would you use a one tailed test?

Ho = mean1 = mean2
Ha = mean 1 ≠ mean2

Answer 2

No

Answer 3

two tailed because we have two directions of interest.
alternative hypothesis is mean is not equal to 75.62.
null hypo is mean is equal to 75.62.
There is evidence that private schools can lead to higher or lower performance on a test of social skills. (type 2 error)
type 2 error = 95%
type 1 error= 5%
if a type 1 error was made then there would be no evidence that private schools can lead higher or lower performance on a test of social skills.