When sample size increases from n = 23 to n = 35, the mean of the distribution of sample means remains same but the standard deviation of the distribution of sample means decreases from 0.073 to 0.059.

Step-by-step explanation:

We are given the amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.5 hours and a standard deviation of 0.35 hour.

Random samples of size 23 and 35 are drawn from the population and the mean of each sample is determined.

Here, $\mu$ = population mean = 7.5 hours

$\sigma$ = population standard deviation = 0.35 hour

Let $\bar X$ = sample mean

(a) The random samples of size of n = 23 is drawn from the population;

So, mean of the distribution of sample means = $\mu$ = 7.5 hours

Standard deviation for the distribution of sample means is given by;

s = $\frac{\sigma}{\sqrt{n} }$ = $\frac{0.35}{23}$ = 0.073

(b) The random samples of size of n = 35 is drawn from the population;

So, mean of the distribution of sample means = $\mu$ = 7.5 hours

Standard deviation for the distribution of sample means is given by;

s = $\frac{\sigma}{\sqrt{n} }$ = $} \frac{0.35}{\sqrt{35} }$ = 0.059

(c) So, as we can see that when sample size increases from n = 23 to n = 35, the mean of the distribution of sample means remains same but the standard deviation of the distribution of sample means decreases from 0.073 to 0.059.

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3 years ago