1. Daily number of claims received by a customer service center are: 68, 100, 83, 78, 8, 65, 24, 81, 92, 48, 35, 75, 73, 13, 75, 51, 71, 12, 56, 97, 31, 96, 97, 58, 63 Assuming the data comes from normal distribution, use critical value approach to test that the mean number of claims is less than 71 per day. Use the level of significance equal to 0.05 and six steps approach to test the hypothesis. Q2. In a recent survey, 20 students were asked whether they wore masks in their recent visits to the shopping center. Their responses as yes (Y) or no (N) are provided below: YYNYNYYNNYNYNY NY NYNN (a) (b) What percentage of students did not wear mask during the last visit? At 1% level of significance, use six steps and p-value approach to test that more than 60% students did not wear mask Q3. Number of bookings in a five start hotel before and after the withdrawal of COVID-19 restrictions are recorded for 20 days. Before 22 55 95 27 45 55 60 50 75 46 94 2 34 47 33 73 47 61 48 72 After 37 72 97 39 63 61 80 63 82 64 106 22 41 60 50 91 62 65 57 89 (a) Assuming the differences due to restriction withdrawal follow normal distribution, construct a 90% confidence interval for mean difference. (b) At 5% level of significance, test that the withdrawal of COVID-19 restriction differs in booking. Q4. An insurance company wants to know if the average speed at which men drive cars is higher than that of women drivers. The company took a random sample of 36 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a standard deviation of 3 miles per hour. Another sample of 18 cars driven by women on the same highway gave a mean speed of 68 miles per hour with a standard deviation of 4 miles per hour. Assume that the speeds at which all men and all women drive cars on this highway are both normally distributed with unequal population standard deviations. (a) Construct a 90% confidence interval for the difference between the mean speeds of cars driven by all men and all women on this highway. (b) Test at the 1% significance level whether the mean speed of cars driven by all men drivers on this highway is higher than that of cars driven by all women drivers. 2 m 2