Question

You provide your boss with a point estimate of 17 and a 95% confidence interval of [13.1,

20.9] for the mean number of armor piercing rounds needed to penetrate a new type of reactive

armor, based on data from 5 trials. Sigma is unknown for this population, so you had to rely on s

in your calculation. She tells you that the range from 13.1 to 20.9 is too wide to be useful and

asks you to narrow it. Legitimate responses to her request include (select two):

a) We can make the range narrower by calculating a 90% confidence interval.

b) We can make the range narrower by calculating a 98% confidence interval.

c) We can conduct additional trials and collect more data; this is guaranteed to narrow the interval.

d) We can conduct additional trials and collect more data; this is likely to narrow the interval.

Answer 1

We know that the confidence interval is dependent on the critical value and sample size

lower confidence level gives lower critical values, which gives us narrower confidence interval

so, option A is correct because 90% confidence level's critical value is smaller than 95% confidence level's critical value.

Increasing the sample size results in decreased margin of error, which decreases the confidence interval width. So, option C is correct

therefore, option A and C are correct