Answer:
The probability of selecting a sample which doesn't capture the true value of μ would be 10% rather than 5% if they decide to calculate a 90% confidence interval rather than a 95% confidence interval from the sample they will select.
Explanation:
The correct answer is the last statement, but first, let's look at the other statements:
Their confidence interval would be less likely to capture the sample mean.
This statement is not correct because the confidence of a confidence interval gives us the probability of capturing the true value of the population mean.
They would decrease the margin of error of their confidence interval if they calculated a 90% rather than a 95% confidence interval.
If we want more confidence we must establish more precision, which means more error. In other words if the confidence increases so does the error for a fixed sample size. The second statement is false.
The probability of selecting a sample which doesn't capture the true value of μ would be 10% rather than 5% if they decide to calculate a 90% confidence interval rather than a 95% confidence interval from the sample they will select.
As stated before the confidence of a confidence interval is the probability that the interval contains the true value of μ. Therefore, if we increase the confidence from 95% to 90% then this probability also increases. A 90% confidence means that there's a 10% probability of not containing the true mean. Likely, a 95% confidence means that there's a 5% probability of not containig the true mean. The third statement is true.