Question

Researchers studying the sticky droplets found on spider webs will measure the widths of a random sample of droplets. From the sample, the researchers will construct a 95 percent confidence interval to estimate the mean width of all such droplets. Write the correct statement about a 95 percent confidence interval for the mean width.

Answer 1

B. The interval will be narrower if the researchers increase the sample size of droplets.

Explanation:

B. The interval will be narrower if the researchers increase the sample size of droplets.

Margin of error of a confidence interval:

The higher the margin of error, the wider an interval is.

In which z is related to the confidence level(the higher the confidence level, the higher z), is the standard deviation of the population and n is the size of the sample.

From this, we conclude that:

If we increase the confidence level, the interval will be wider.

If we increase the sample size, the interval will be narrower.

Which of the following statements about a 95 percent confidence interval for the mean width is correct?

Increasing the sample size leads to a narrower interval, so the correct answer is given by option B.

Answer 2

The interval will be narrower if the researchers increase the sample size of droplets.

Explanation:

The confidence interval can be obtained using the relation :

Xbar ± Margin of error

Margin of Error = Zcrit * s/sqrt(n)

Zcritical = critical vlaue at the specified α - level

n = sample size ; s = standard deviation

Sample size being the denominator, will reduce the overall value of the error margin as we utilize a larger sample.

Hence, the interval becomes narrower as the error margin is reduced which is achieved by employing an increased sample size.