Question

Problem 2. The data below gives the mean price (in cents) of a litre of regular gasoline at self-service filling stations at a sample of six urban centres in Canada in May 2012. Urban area Halifax Saint John, NB Toronto Thunder Bay Winnipeg Victoria Price/litre 131.5 129.7 128.9 138.2 122.1 131.8 Provide answers to the following to two decimal places. Part (a) Find the sample mean (in cents). Part (b) Find the sample standard deviation (in cents). Part (c) Using the appropriate t distribution, find a 90% confidence interval for the mean gasoline price per litre across urban Canada in May 2012. Provide the upper and lower bounds for your confidence interval. ( Part (d) Would a 95% confidence interval be wider or narrower than the interval you found in Part (c)? Using the appropriatet distribution, find a 95% confidence interval for the mean gasoline price per litre across urban Canada in May 2012. Provide the upper and lower bounds for your confidence interval.(

Answer 1

solution:-

part (a) sample mean = 130.37

part (b) sample standard deviation 5.21

part (c)

here degree of freedom df = n - 1 = 6 - 1 = 5

we look into t table with df and with 90% confidence

critical value t = 2.015

confidence interval formula

=> sample mean +/- t * standard deviation/sqrt(n)

=> 130.37 +/- 2.015 * 5.21/sqrt(6)

=> (126.08 , 134.66)

part (d)

here degree of freedom df = n - 1 = 6 - 1 = 5

we look into t table with df and with 95% confidence

critical value t = 2.571

confidence interval formula

=> sample mean +/- t * standard deviation/sqrt(n)

=> 130.37 +/- 2.571 * 5.21/sqrt(6)

=> (124.90 , 135.84)

the confidence interval be wider than the interval found in part(c)