Question

Students in a statistics class conduct a survey to estimate the mean number of units students at their college are enrolled in. The students took a random sample of 50 students from their college. The students calculated a 90% confidence interval to estimate the mean number of units students at their college are enrolled in. The confidence interval was too wide to provide a precise estimate. The students are strategizing about how to produce a narrower confidence interval. True or false? The students could produce a narrower confidence interval by increasing the sample size to 100.

Answer 1

Answer: Students in a statistics class conduct a survey to estimate the mean number of units students at their college are enrolled in. The students took a random sample of 50 students from their college. The students calculated a 90% confidence interval to estimate the mean number of units students at their college are enrolled in. The confidence interval was too wide to provide a precise estimate. The students are strategizing about how to produce a narrower confidence interval. True or false? The students could produce a narrower confidence interval by increasing the sample size to 100.

Step-by-step explanation:

Answer 2

Answer:

True

Step-by-step explanation:

The margin of error of a confidence interval is given by:

$M = z*\frac{\sigma}{\sqrt{n}}$

In which z is the critical value related to the confidence level, $\sigma$ is the standard deviation of the population and n is the size of the sample.

So as n increases, the margin of error decreases, that is, the interval gets narrower.

The students could produce a narrower confidence interval by increasing the sample size to 100.

From the explanation above, the answer is true.