Question 3 Total 25 Marks An insurance company claims that average speed at whic

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Question 3 Total 25 Marks An insurance company claims that average speed at which men drive cars is greater than that of women drivers. In order to verify this, the company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a variance of 4.84 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 variance of 6.25 miles per hour. Assume that the speeds at which all men and women drive cars on this highway are both normally distributed with the same population standard deviation. (a) Construct a 90% confidence interval for the population mean speed of men driving on 9 marks] (b) Test at 1% significance level whether the claim of the insurance company is true. [16 marks] this highway

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Question 3 Total 25 Marks An insurance company claims that average speed at which men drive cars is greater than that of women drivers. In order to verify this, the company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a variance of 4.84 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 variance of 6.25 miles per hour. Assume that the speeds at which all men and women drive cars on this highway are both normally distributed with the same population standard deviation. (a) Construct a 90% confidence interval for the population mean speed of men driving on 9 marks] (b) Test at 1% significance level whether the claim of the insurance company is true. [16 marks] this highway

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