A survey of 25 randomly selected customers found the ages shown (in years). The

Question

A survey of 25 randomly selected customers found the ages shown (in years). The mean is 32.72 years and the standard deviation is 9.79 years a) What is the standard error of the mean? b) How would the standard error change if the sample size had been 225 instead of 25? (Assume that the sample standard deviation didn't change.) 21 38 34 28 30 33 11 41 48 49 25 33 23 34 21 38 33 46 28 34 19 45 37 25 44 IS a) The standard error of the mean is (Round to two decimal places as needed.) b) How would the standard error change if the sample size was 225 instead of 25 with the same sample standard deviation? Select the correct choice below and fill in any answer boxes within your choice. O A. The standard error would increase. The new standard error would betimes the old B. The standard error would decrease. The new standard error would be the old standard error divided by ° C. The standard error would not change

Explanation / Answer

(a)The SE = Standard deviation / Sqrt(sample size) = 9.79/Sqrt(25) = 1.96

(b) Since the sample size is in the denominator, an increase in sample size, will decrease the SE.

Now, the new sample size = 225 = 25 * 9. The old sample error was 9.79/Sqrt(25),

The new SE will be = 9.79/[Sqrt(25)*Sqrt(9)] = Old SE/Sqrt(9) = Old SE/3.

Therefore Option B. The SE would decrease. The new SE would be the old standard error divided by 3.

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