Find a 90% confidence interval for the mean if a sample of size 12 has a mean =

Question

Find a 90% confidence interval for the mean if a sample of size 12 has a mean = 34.2 and the standard deviation ? = 8.5.

(31.06, 37.34)

(30.16, 38.24)

(29.79, 38.61)

(31.99, 36.41)

10 points

Question 7

Refer to Problem # 6. If you kept all other values the same and increased the sample size n, what would happen to the interval?

The error would be smaller, making the confidence interval narrower.

The error would be larger, making the confidence interval wider.

The error would be larger, making the confidence interval narrower.

The error would be smaller, making the confidence interval wider

I know six is the second answer, I need the answer to 7 :)

(31.06, 37.34)

(30.16, 38.24)

(29.79, 38.61)

(31.99, 36.41)

Explanation / Answer

Answer to 7.

If you kept all other values the same and increased the sample size n, the width of the confidence interval decreases and also it decreases the standard error. Also, with bigger sample sizes, the sample mean becomes a more accurate estimate of the parametric mean, so the error becomes smaller.

The option one is the answer : the error would be smaller, making the confidence interval narrower.

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