Question

In 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from the CDC. Suppose that a random sample of 45 women who are 20 years of age or older in 2015 results in a mean height of 63.6 inches with a standard deviation of 0.5 inch. Now we want to perform a hypotheses test to check whether the women today are lower than in 1990 at the 0.05 level of significance based on this sample.

62. Which of the followings is the type I error in this problem?

A. Claim the population mean height is lower than 63.7 inches while it is actually 63.7 inches.

B. Claim the population mean height is equal to 63.7 inches while it is lower than 63.7 inches.

C. Claim the population mean height is taller than 63.7 inches while it is actually 63.7 inches.

D. Claim the population mean height is equal to 63.7 inches while it is taller than 63.7 inches.

63. Which of the followings is the type II error in this problem?

A. Claim the population mean height is lower than 63.7 inches while it is actually 63.7 inches.

B. Claim the population mean height is equal to 63.7 inches while it is lower than 63.7 inches.

C. Claim the population mean height is taller than 63.7 inches while it is actually 63.7 inches.

D. Claim the population mean height is equal to 63.7 inches while it is taller than 63.7 inches.

Answer 1

Here as given

  mean height = = 63.6 inches

standard deviation= s =  0.5 inch.

So here hypothesis are

H0 : = 63.7 inches

Ha : < 63.7 inches

Question 62

Here type I error is  Claim the population mean height is lower than 63.7 inches while it is actually 63.7 inches. Option A is correct here.

Question 63

Here type II error is  Claim the population mean height is actually  63.7 inches while it is less than 63.7 inches. Option B is correct here.