Question

If everything else stays the same, the margin of error can be reduced by (select all that are true) :

a. increasing confidence level

b. decreasing sample size

c. increasing sample size

d. decreasing confidence level

Answer 1

Answer: c. increasing sample size

d. decreasing confidence level

Explanation:

Formula for margin of error :

`E=z(\sigma)/(√(n))` ,
`\sigma` = Population standard deviation.

`E=t(s)/(√(n))` , s= sample standard deviation.

`E=z\sqrt{(p(1-p))/(n)}`, p= sample proportion.

Here z and t are critical values.

n= sample size.

Margin of error has critical t-value of z-value in the numerator .

⇒ Margin of error is proportional to the critical value.

⇒ Margin of error is proportional to the confidence level.

(The critical t-value of z-value is proportional the confidence level increases.)

So , Margin of error can be reduced by decreasing confidence level.

Also , Margin of error has square root of the sample size in the denominator.

⇒ Margin of error is inversely proportional to the sample size.

So , Margin of error can be reduced by increasing sample size.

Hence, the correct options area :

c. increasing sample size

d. decreasing confidence level