(Solved): please answer problem 4: questions 1) to 9) with detailed steps. thank you  Sample Problem 4 A ...

Sample Problem 4 A social psychologist is interested in gender differences in the sociability of teenagers. Using the number of good friends as an indicator of sociability, the researcher found that females had on average \( 5.9 \) close friends ( \( s=3.1 ; n=44) \) and males had on average \( 4.8 \) close friends \( (s=4.2 ; n=35) \). Is the difference in the sociability observed between males and females significant at a \( 95 \% \) confidence level? 1. Write a question that will generate interval/ratio data on the number of good friends. 2. What hypothesis test should be done to answer this research question? a. A two-independent sample t-test b. A one sample \( t \) test c. A paired t test d. An analysis of variance (ANOVA) \( \mathrm{F} \) Test 3. Is this a one-or a two-tailed test? 4. State the Null and Research Hypotheses 5. What is the significance level \( (\alpha) \) ? 6. What are the degrees of freedom (df)? 7. The \( \mathrm{p} \)-value is calculated to be \( \mathbf{0 . 3 8 1} \). 8. Should the null hypothesis be retained or rejected? Why? 9. Interpret the results in relation to the research question.