In a sociology class, an instructor asks her students how many hours per week they spend on social networks. She wants to investigate whether time spent on social networks differs for male and female students at this university. For a randomly selected group of females and males, those aged 21 or under, drawn from normally distributed populations with known and equal variance of 9, the following results were obtained:
Males: 5, 7, 9, 10, 12, 12, 12, 13, 13, 15, 15, 20
Females: 5, 7, 7, 8, 10, 10, 11, 12, 12, 14, 14, 14, 16, 18, 20, 20, 20, 22, 23, 25, 40
1. Conduct a hypothesis test to determine whether the population mean number of hours spent on social networks differs between males and females. Include all assumptions, hypotheses, test statistic, and p-value, and interpret the result in context.
2. For which significance levels can you reject H0? (i) 0.10, (ii) 0.05, or (iii) 0.01.
3. Based on the answers in part 2), for which confidence levels would the confidence interval contain 0? (i) 0.90, (ii) 0.95, or (iii) 0.99.
4. Use part 2) and part 3) to illustrate the correspondence between results of significance tests and results of confidence intervals. Please use corresponding formulas and solve the question step by step.