Question 3, 10.4.52 A random sample of 10 students were surveyed on their social activities. The students were asked to state how many times during the previous year they had gone to a movie, sporting event, orparty. The accompanying table shows the responses. Complete parts a through d below.Click the icon to view the data for attending movies, sporting events, and parties.a. Find and interpret a 95% confidence interval for the difference in the mean number of events attended for parties and sporting events. Define the difference as the number of parties minus thenumber of sporting events.The 95% confidence interval is D.(Round to two decimal places as needed.) Croquonou of Attending Movies, Sports Events, and PartiesFrequency of Attending Movies, Sports Events, and PartiesFrequency of Attending Movies, Sports Events, and PartiesActivitySports3417Student12345678910Movies9121502-2618733=241287 SNHN49291123Parties112652502254J

The objective is to find and interpret 95% confidence interval for the difference in the mean number of events attended for parties and sporting events. The difference is the number of parties minus the number of sporting events. Calculations: Student Parties Sports Difference (d) 1 26 3 23 2 14 4 10 3 7 17 -10 4 52 11 41 5 8 1 7 6 27 8 19 7 50 7 43 8 2 23 -21 9 25 3 22 10 4 11 -7 ∑di=127 Mean of the differences is: d¯=∑din=12710=12.7 Standard deviation of the differences is computed as: sd=∑di-d¯2n-1=23-12.72+10-12.72+-10-12.72+41-12.72+7-12.72+19-12.72+43-12.72+-21-12.72+22-12.72+-7-12.7210-1=21.16102 The required confidence interval is computed using the formula: C.I=d¯±t*sdn where t* is the t-critical value at degrees of freedom df=10-1=9 and confidence level 95%. Using the t-table, the required t critical value is 2.262 Substitute the values in the formula: C.I=d¯±t*sdn=12.7±2.26221.1610210=12.7±15.13663011=12.7-15.13663011, 12.7+15.13663011≈-2.44, 27.84 Thus, the 95% confidence interval is (-2.44, 27.84) Interpretation: There is 95% confidence that the mean difference in the number of events attended for parties and sporting events lies between -2.44 and 27.84.