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.

Question

Mathematics

Sawyer Blackwell

26 February, 14:51

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.

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Conan · Answer 1

Step-by-step explanation:

The formula for determining confidence interval is expressed as

Confidence interval

= mean ± z * s / √n

Where

z is the value of the z score

s = standard deviation

n = sample size

a) The 95 % confidence level has a z value of 1.96

The 99 % confidence level has a z value of 2.58

Since 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.