A simple random sample of 50 female 14-year-olds is selected. The sample mean height of the girls is found to be 62 inches. Assume the height of 14-year-old girls is normally distributed with a standard deviation of 5 inches.

Question

1. Based on these data, a 95% confidence interval for the true mean height of all
14-year-old girls is:
A) 62 +/- 1.96
B) 62 +/- 1.386
C) 62 +/- 1.645
D) 62 +/- 0.196
2. Which of the following correctly interprets the 95% confidence interval for the true
mean height of all 14-year-old girls?
A) We can be 95% confident that the sample mean height of 14-year-old girls is within
the confidence interval obtained.
B) If this study were to be repeated with a sample of the same size, there is a 0.95
probability that the sample mean height of 14-year-old girls would be in the interval
obtained.
C) We can be 95% confident that the population mean height of all 14-year-old girls is
within the interval obtained.
D) 95% of all 14-year-old girls have heights within the interval obtained.

Answer 1

1. 95% = mean ± 1.96SEm

SEm = SD/√n

2. C

Answer 2

kik