Question

Suppose that we wanted to estimate the true average number of customers at a particular restaurant with 95% confidence. The margin of error we are willing to accept is 2. Suppose we also know that the population standard deviation is 10. Increasing our confidence to 97% will _____.

(A) increase the margin of error
(B) cause the required sample size to decrease
(C) not affect the required sample size
(D) decrease the margin of error
(E) cause the required sample size to increase

Answer 1

Correct option (A).

Increasing our confidence to 97% will increase the margin of error.

Explanation:

The confidence interval for population mean is:

`\bar x\pm z_(\alpha/2)(\sigma)/(√(n))`

The margin of error is:

`MOE = z_(\alpha/2)(\sigma)/(√(n))`

The margin of error of is directly proportional to the critical value.

`MOE\propto z_(\alpha /2)\\`

So if the confidence level is increased from 95% to 97% the critical value will increase.

• The critical value of z for 95% confidence level is 1.96.

• The critical value of z for 97% confidence level is 2.17.

If the critical values increases the MOE increases.

Thus, on increasing the confidence level to 97% the margin of error will increase.