The amounts of time employees at a large corporation work ea

The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.7 hours and a standard deviation of 0.33 hour. Random samples of size 23 and 34 are drawn from the population and the mean of each sample is determined. What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases? If the sample size is n = 23, find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means is .(Type an integer or a decimal.) The standard deviation of the distribution of sample means is . (Round to two decimal places as needed.) lithe sample size is n = 34, find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means is . (Type an integer or a decimal.) The standard deviation of the distribution of sample means is . (Type an integer or decimal rounded to the nearest hundredth as needed.) What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases? Choose the correct answer below. A. The mean stays the same, but the standard deviation increases. B. The mean stays the same, but the standard deviation decreases. C. The mean and the standard deviation both increase. D. The mean and the standard deviation both decrease.

Solution

When n=23

Mean = 7.7
S.d = 0.33/Sqrt(23) = 0.068

When n=34
Mean = 7.7
S.d = 0.33/Sqrt(34) = 0.0565

The mean stays same , but the standard ddeviation decreases