Problem (1) Solve using the formula (Handwrite your solutionProblem )

Maine Mountain Dairy claims that its eight-ounce low-fat cups contain, on average, fewer calories than the eightounce low-fat yogurt cups produced by a competitor. A consumer agency wanted to check this claim. A sample of 50 such yogurt cups produced by this company showed that they contain d an average of 141 calories per cup with a standard deviation of 5.5 calories. A sample of 40 such yogurt cups produced by its competitor showed that they contained an average of 144 calories per cup with a standard deviation of 6.4 calories.

a. Test the 2% significance level whether Main Mountain Dairy's claim is true.

b. Calculate the p-value for the test of part a. Based on this p-value, would you reject the null hypothesis if =0.005? What if = 0.025?

The drawing of the normal curve (by Excel or by hand) must be properly labeled showing the critical (rejection) region and the noncritical(acceptance) regions.