The amounts of time employees at a large corporation work each day are normally
ID: 3061503 • Letter: T
Question
The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.4 7.4 hours and a standard deviation of 0.37 0.37 hour. Random samples of size 26 26 and 35 35 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 equals = 26 26, find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means is nothing . (Type an integer or a decimal.) The standard deviation of the distribution of sample means is nothing . (Round to two decimal places as needed.) If the sample size is n equals = 35 35, find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means is nothing . (Type an integer or a decimal.) The standard deviation of the distribution of sample means is nothing . (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 and the standard deviation both increase. B. The mean stays the same, but the standard deviation decreases. C. The mean and the standard deviation both decrease. D. The mean stays the same, but the standard deviation increases.
Explanation / Answer
Result:
The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.4 hours and a standard deviation of 0.37 hour. Random samples of size 26 and 35 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 equals = 26 , find the mean and standard deviation of the distribution of sample means.
The mean of the distribution of sample means is 7.4 . (Type an integer or a decimal.)
The standard deviation of the distribution of sample means is 0.07 . (Round to two decimal places as needed.)
Standard error = sd/sqrt(n) = 0.37/sqrt(26) =0.072563
If the sample size is n equals = 35 , find the mean and standard deviation of the distribution of sample means.
The mean of the distribution of sample means is 7.4 . (Type an integer or a decimal.)
The standard deviation of the distribution of sample means is 0.06 . (Type an integer or decimal rounded to the nearest hundredth as needed.)
Standard error = sd/sqrt(n) = 0.37/sqrt(35)= 0.062541
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 and the standard deviation both increase.
Answer: B. The mean stays the same, but the standard deviation decreases.
C. The mean and the standard deviation both decrease.
D. The mean stays the same, but the standard deviation increases.
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