Question

A random sample of 200 adult residents in the U.S reveals that the mean minutes of sleep they received the night prior to the interview was 528 minutes with a standard deviation of 141 minutes. Using a computer, a random sample of 200 observations was taken (with replacement) from these data and an average was computed and recorded. This was repeated 10,000 times and a visualization was made of this sampling distribution. The mean of the sampling distribution was 528 minutes and the standard deviation was 10 minutes. The sampling distribution was symmetric and unimodal. Which of the following is an approximate 95% confidence interval for the mean amount of sleep of all US residents?
a. Lower bound: 528-141, upper bound: 528+141; (387, 669)
b. Lower bound: 528-10, Upper bound: 528+10; (518,538)
c. Lower bound: 528-20141, upper bound: 528 * 2*141; 246,810)
d. lower bound: 528-2-10, upper bound: 528+2*10; (508, 548)

Answer 1

Answer:

d. lower bound: 528-2-10, upper bound: 528+2*10; (508, 548)

Step-by-step explanation:

The computation of the approximate 95% confidence interval is shown below:

Given that

mean = 528,

standard deviation = 10

$Mean \mp z_{\frac{0.05}{2}}\times standard\ deviation \\\\=528 \mp 2 \times 10\\\\=(508,548)$

hence, the correct option is d.