State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else changes.) a. Changing from a 95% confidence level to a 99% confidence level. b. Changing from a sample size of 15 to a sample size of 350. c. Changing from a standard deviation of 15 pounds to a standard deviation of 20 pounds.
Accepted Solution
A:
Answer:Step-by-step explanation:The formula for determining confidence interval is expressed as Confidence interval = mean ± z × s/ √nWhere z is the value of the z scores = standard deviationn = sample sizea) The 95% confidence level has a z value of 1.96The 99% confidence level has a z value of 2.58Since 99% confidence level z value is greater than 95% confidence level z value, if we input it into the formula, it will result to a higher confidence interval. So changing from a 95% confidence level to a 99% confidence level would make a confidence interval wider.b) The √15 is smaller than the √350. This means that if we make use of the formula, √350 will give a lower confidence interval than that of √15. Therefore, the confidence interval would be narrower changing from a sample size of 15 to a sample size of 350.c) Applying the formula, a standard deviation of 15 pounds would result to a lower confidence interval than a standard deviation of 20 pounds. Therefore, the confidence interval would be wider changing from a standard deviation of 15 pounds to a standard deviation of 20 pounds.