1. Assume the price of gas across gas stations in Boston at any particular time has a normal distribution with unknown mean and variance. In order to estimate the expected price on a given day, you drive to 4 nearby stations and record their prices per gallon as $1.99, $2.29, $1.99, and $1.99. – Compute a 95% confidence interval for the expected price for a gallon of gas. – Assume now that I tell you that the population standard deviation of gas prices across different stations is known to be 15 cents. How will this information change your 95% confidence interval? Explain. 2. Refer to the June 2007 survey on satellite radio subscriber service and usage conducted for the National Association of Broadcasters, a random sample of 501 satellite radio subscribers were asked, “Do you have a satellite radio receiver in your car?” The survey found that 396 subscribers did, in fact, have a satellite receiver in their car a. From the sample, calculate an estimate of the true proportion of satellite radio subscribers who have a satellite radio receiver in their car. b. Form a 90% confidence interval for the estimate, part a. c. Give a practical interpretation of the interval for the estimate, part b.