Answer the questions below

A researcher was interested in whether the 15,196 employees at her company were more or lessintelligent compared to the national average, so she administered the Wechsler Adult Intelligence Test (WAIS) to a random sample of 81 employees and they scored an average of 105 with a standard deviation of 16. The national average on the WAIS is a score of 100 and higher scores indicate higher intelligence.

1. Would she need a one-tailed test or a two-tailed test to answer her question?

2. What is the null hypothesis (in words or formula)?

3. What is the alternative hypothesis (in words or formula)?

4. What would be the shape of the sampling distribution of the mean? Explain your answer.

5. Using the sample standard deviation (16) to estimate the population standard deviation, what would the standard error of the mean be for the sampling distribution of the mean?

6. What is the Z score on the sampling distribution of the mean for a mean score of 105, if the null hypothesis is true?

7. What is the probability of getting a sample mean of 105?

8. Would the researcher fail to reject the null hypothesis or reject the null hypothesis?

9. What would be more likely that the researcher committed a Type 1 error or a Type 2 error?