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5. The computer science professors at UW are curious about whether male or female professors, on average, have more Facebook friends. The data for the professors is displayed below. Gender n x Male 68 678.9 Female 91 616.1 Construct a 95% confidence interval for the difference in mean number of Facebook friends for male and female professors at this university. The standard error is 51.81. Use two decimal places in your margin of error. Interpret your answer in context, specically stating whether or not there is a difference. 6. Using the same context and data in #5, test (at the 5% level] if this sample provides evidence of a significant difference in the mean number of Facebook friends for male and female professors at this university. Include all of the details of the test. a. Define the appropriate parameterts} and state the hypotheses for testing if the mean number of Facebook friends is different between the male and female professors. b.ldentify {using the appropriate notation] the sample statistic for this sample. c. What type of test would you use on StatKey? (circle one} Left Tail Two Tail Right Tail d.Use a p-value of 0.23 to make a decision about these hypotheses. Be sure to word your decision in the context of the