Question

There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious apples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence?A. (–0.076,0.236)B. (–0.105,0.265)C. (–10.5,26.5)D. (–76,236)E. (−105,265)

Answer 1

(E) (−105,265)

Explanation:

The 98 percent confidence interval for the difference in proportions of apples with blemishes is (−0.105,0.265). The interval estimate for the difference in the numbers of apples with blemishes is found by multiplying the endpoints of the interval for the proportion by 1,000.

Answer 2

48/75 = 0.64

42/75 = 0.56

The z score for 98% level of confidence is 2.326

The interval:

0.64 - 0.56 +/ - 2.326 x sqrt(0.64 (1-0.64)/75 + (0.56(1-0.56)/75))

= 0.08 + 0.185 & 0.08 - 0.185

Interval = (-0.105, 0.265)