Question

If all other factors are held constant, increasing the sample size willa. increase the estimated standard errorb. decrease the width of the confidence intervalc. increase the width of the confidence intervald. none of the above

Answer 1

Answer:

b. decrease the width of the confidence interval

True. For this case the width is given by:

$Width = 2 ME= 2 z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

And if we see since we are increasing the sample size (value of n) then the margin of error would be lower and then the width of the interval will decrease

Step-by-step explanation:

If all other factors are held constant, increasing the sample size will

We can analyze the situation one by one

a. increase the estimated standard error

For this case the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}$

False, we can't increase the standard error, increasing the denominator.

b. decrease the width of the confidence interval

True. For this case the width is given by:

$Width = 2 ME= 2 z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

And if we see since we are increasing the sample size (value of n) then the margin of error would be lower and then the width of the interval will decrease

c. increase the width of the confidence interval

False. For this case the width is given by:

$Width = 2 ME= 2 z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

And if we see since we are increasing the sample size (value of n) then the margin of error would be lower and then the width of the interval will decrease and not increase

d. none of the above

False. Option c is correct.