Answer:
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, = population mean = 7.5 hours
= population standard deviation = 0.35 hour
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<u><em>Let </em></u><u><em> = sample mean</em></u>
(a) The random samples of size of n = 23 is drawn from the population;
So, mean of the distribution of sample means = = 7.5 hours
Standard deviation for the distribution of sample means is given by;
s = =
= 0.073
(b) The random samples of size of n = 35 is drawn from the population;
So, mean of the distribution of sample means = = 7.5 hours
Standard deviation for the distribution of sample means is given by;
s = =
= 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.