In a study of social media habits, a company finds that their population of users write μ = 9.2 messages per week (σ = 4.4). A researcher finds that a sample of teenagers (n = 55) send X̅ = 10.3 messages per week. Because this social media company markets itself to young people, the researcher thinks that teenagers may be more likely to send more messages than the average user. Conduct a z-test on these data.

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. Should the researcher conduct a one- or a two-tailed test?

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 researcher reject or retain the null hypothesis? Does this mean that teenagers send more messages, fewer messages, or approximately the same number of messages as the population of social media users?

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 α were .05 and the sample size were increased to 75, would the researcher reject or retain the null hypothesis?