Question

7. Pierre's is interested in comparing the calorie amounts of its cherry and cheese Danish. A sample of 18 cherry Danish had an average of 356.25 calories, with a standard deviation of 7.22, while a sample of 14 cheese Danish had an average of 365.88 calories, with a standard deviation of 8.41. Find a 90% confidence interval to estimate the difference in the calorie amounts between the two types of Danish and explain what your interval means. (13 pts)

Answer 1

Solution: Cherry Danish: n1 18 S1 7.22 1 = 356.25 Cheese Danish: n2 = 14 S2 8.41 X2=365.88 Degrees of Freedom: 2 2 n2 df 2 2 il Si 1n2 1n1 2 (7.222 18 8.412 14 df 2 7.222 + 2 8.412 1 1 18 1 18 = 25.7 25(Rounding down) 14 1 14 df For 90% confidence interval, a 1-0.90 0.10 a/2 0.10/2 = 0.05 From t-distribution table, the value of t having an area of (a/2 0.05) in its upper tail and for (df = 373) is given by to.o5 = 1.708

Margin of Error: MoE = to.05 X 7.222 8.412 MoE 1.708 x 18 14 MoE 4.816 90% confidence interval of the difference in calorie amounts: (356.25 365.88) 4.816 -9.63 t 4.816 Lower limit of 90% confidence interval-9.63 -4.816 -14.446 Upper limit of 90% confidence interval -9.634.816 -4.814 The above interval limits imply that we are 90% confident that the mean amount of calories in cheese Danish is more than the mean amount of calories in cherry Danish by 4.814 to 14.446