Question

You have information on the average number of hours spent studying and playing videogames for children who play sport, and children who do not play sport. The following table gives the average number of hours spent studying, the average number of hours spent on videogames, and the standard deviations of these two variables for your two samples. The two sample sizes are in the row called "Observations". Children who Children who play sport do not play sport Mean St. Dev. Mean St. Dev. Hours spent studying 9.5 10.1 4.5 Hours spent on videogames 8.2 Observations 1,321 936 3.2 4.0 036 (a) Describe the appropriate null and alternative hypotheses for testing whether: • (0) Children who play sport spend the same number of hours studying than those who do not play sport. (i) Children who play sport spend the same number of hours playing videogames than those who do not play sport. (5 marks] (b) Carry out significance tests (using a 5% level of significance) to test these hypotheses (also state which critical value you are using and why). [10 marks] (c) Find the 95% confidence interval for the difference in means for each hypothesis. [5 marks] (d) Interpret the results of the confidence intervals. What do we conclude? [5 marks) (e) How would the confidence intervals look like if the two tests had not rejected the Null Hypothesis? 15 marks]