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1 answer:
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Answer:
(a): The 95% confidence interval is (46.4, 53.6)
(b): The 95% confidence interval is (47.9, 52.1)
(c): Larger sample gives a smaller margin of error.
Step-by-step explanation:
Given
-- sample size
-- sample mean
--- sample standard deviation
Solving (a): The confidence interval of the population mean
Calculate the standard error
The 95% confidence interval for the z value is:
Calculate margin of error (E)
The confidence bound is:
--- approximated
--- approximated
<em>So, the 95% confidence interval is (46.4, 53.6)</em>
Solving (b): The confidence interval of the population mean if mean = 90
First, calculate the standard error of the mean
The 95% confidence interval for the z value is:
Calculate margin of error (E)
The confidence bound is:
--- approximated
--- approximated
<em>So, the 95% confidence interval is (47.9, 52.1)</em>
Solving (c): Effect of larger sample size on margin of error
In (a), we have:
In (b), we have:
<em>Notice that the margin of error decreases when the sample size increases.</em>