Conduct a z-test for a dataset where = 114.6, = 13.2, X = 109.4, and

Conduct a z-test for a dataset where μ = 114.6, σ = 13.2, X̅ = 109.4, and n = 88.

a. What are the groups for this z-test?

b. What is the null hypothesis for this z-test?

c. What is the value of α?

d. Is a one-tailed test or a two-tailed test appropriate for this situation?

e. What is the alternative hypothesis?

f. What is the z-observed value?

g. What is(are) the z-critical value(s)?

h. Based on the critical and observed values, should the null hypothesis be rejected or retained?

i. What is the p-value for this example?

j. What is the Cohen’s d value for this example?

k. If the α value were dropped to .01, would the researcher reject or retain the null hypothesis?

l. If the α value were raised to .10, would the researcher reject or retain the null hypothesis?

m. If α were .05 and the sample size were increased to 140, would the researcher reject or retain the null hypothesis?

n. If α were .05 and the sample size were decreased to 45, would the researcher reject or retain the null hypothesis?

o. If α were .05 and the sample size were decreased to 15, would the researcher reject or retain the null hypothesis?