Question

A researcher is planning to construct a one-sample z?confidence interval for a population mean ?. Select the statements that would lead to a smaller margin of error, assuming the other factors remain the same.A) The population standard deviation turns out to be higher than expected.B) The researcher increases the sample size.C) The researcher lowers the confidence level.D) The researcher decreases the sample size.E) The population standard deviation turns out to be lower than expected.F) The researcher raises the confidence level.

Answer 1

Answer:

B

C

E

Step-by-step explanation:

The margin of error of the confidence interval for a normally distributed population is given by the following formula:

$M = z*\frac{\sigma}{\sqrt{n}}$

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

Lets analize each option:

A) The population standard deviation turns out to be higher than expected.

If the standard deviation $\sigma$ is higher than expected, M is also going to be higher. This means that the margin of error will be higher. So this option is wrong.

B) The researcher increases the sample size.

If n is increased, M will decrease. So this is going to lead to a smaller margin of error. This is a correct option.

C) The researcher lowers the confidence level.

The lower the confidence level is, the lower the value of M is. So it does lead to a smaller margin of error, being a correct option.

D) The researcher decreases the sample size.

If n is decreased, M increases, leading to a higher margin of error. This option is wrong.

E) The population standard deviation turns out to be lower than expected.

If the standard deviation $\sigma$ is lower than expected, M is also going to be lower. This means that the margin of error will be lower. So this option is correct.

F) The researcher raises the confidence level.

The higher the confidence level is, the higher the value of M is. So it does lead to a higer margin of error, being a wrong option.