Maine Mountain Dairy claims that its 8-ounce low-fat yogurt cups contain, on average, fewer calories than the 8-ounce low-fat yogurt cups produced by a competitor. A consumer agency wanted to check this claim. A sample of 27 such yogurt cups produced by this company showed that they contained an average of 141 calories per cup. A sample of 25 such yogurt cups produced by its competitor showed that they contained an average of 144 calories per cup. Assume that the two populations are normally distributed with population standard deviations of 5.5 and 6.4 calories, respectively.
a. Make a 98% confidence interval for the difference between the mean number of calories in the 8-ounce low-fat yogurt cups produced by the two companies.
b. Test at a 1% significance level whether Maine Mountain Dairy’s claim is true.
c. Calculate the p-value for the test of part b. Based on this p-value, would you reject the null hypothesis if α = .05? What if α = .025?