Tina's science fair project was to estimate the mean amount of chemicals in her city's water supply. At first, she had decided to use a random sample of 15 observations. But her teacher asked her to take 35 observations. The mean and standard deviation from 35 observations turned out to be approximately the same as those from 15 observations. Is there any advantage in using 35 observations instead of 15 observations?
A.
There is no advantage. Because the mean and the standard deviation are about the same, the confidence interval computed using 35 observations should be approximately the same as that computed using 15 observations.
B.
There is no advantage. In fact, the 20 extra observations will increase the likelihood of error.
C.
There is no advantage. Because she took 35 observations instead of 15 observations, the confidence interval using 35 observations will be wider than that using 15 observations.
D.
There is some advantage. Because she took 35 observations instead of 15 observations, the confidence interval using 35 observations will be narrower than that using 15 observations.
E.
There is some advantage. With 35 observations, she will be able to compute an exact \(z\)-confidence interval instead of an approximate \(t\)-confidence interval.
Exam No：AP Statistics Problem Set 11 Year：2024 Question No：APStatistics2024AP0451
Answer:
D
Knowledge points:
3.3 Random Sampling and Data Collection
5.5 Sampling Distributions for Sample Proportions
6.2 Constructing a Confidence Interval for a Population Proportion
Solution:
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