A sample of 250 auto drivers selected from a large city showed that they pay on average $128 auto insurance premium per month with a standard deviation of $18. (i) Construct a 97% confidence interval for the mean monthly auto insurance premium paid by auto drivers of that city. (ii) Suppose the confidence interval obtained in part (i) is too wide. How can you reduce the width of this interval? Which of the possible alternatives is the best and why?
(b) A random sample of 25 housewives showed that they spend an average of 35 hours a week on household chores with a standard deviation of 4.5 hours. Assume that the number of hours spend on household chores by all housewives has an approximate normal distribution. Construct a 99% confidence interval for the mean number of hours spent on household chores by all housewives and interpret the confidence interval.
Answers
Answer:
(a) A sample of 250 auto drivers selected from a large city showed that they pay on average $128 auto insurance premium per month with a standard deviation of $18.
(i) Construct a 97% confidence interval for the mean monthly auto insurance premium paid by auto drivers of that city.
(ii) Suppose the confidence interval obtained in part (i) is too wide. How can you reduce the width of this interval? Which of the possible alternatives is the best and why?
(b) A random sample of 25 housewives showed that they spend an average of 35 hours a week on household chores with a standard deviation of 4.5 hours. Assume that the number of hours spend on household chores by all housewives has an approximate normal distribution. Construct a 99% confidence interval for the mean number of hours spent on household chores by all housewives and interpret the confidence interval.