Dr. Cyril conducts a simple random sample of 500 men who became fathers for the first time in the last year. He finds that 23% of them report being unsure of their ability to be good fathers, plus or minus 4%. If Dr. Cyril increased his sample size to 1,000, which of the following would happen?

a. the true estimate would increase

b. the margin of error would become smaller

c. external validity would become less important

d. statistical validity would become negatively affected

The margin of error would become smaller

If Dr. Cyril increases his sample size from 500 to 1,000, the correct answer is b. the margin of error would become smaller.

The margin of error is directly related to the sample size in a random sample. As the sample size increases, the margin of error decreases, assuming all other factors remain constant.

Here’s a more detailed explanation:

a. The true estimate would not necessarily increase. The estimate (23% in this case) is an approximation of the true population parameter, and increasing the sample size does not automatically change the estimate itself. A larger sample size may result in a slightly different estimate, but it is not guaranteed to increase or decrease.

b. The margin of error would become smaller. The margin of error is a measure of the precision of the estimate and is calculated based on the sample size. A larger sample size typically results in a smaller margin of error, assuming the same confidence level and population variability. In this case, increasing the sample size from 500 to 1,000 would decrease the margin of error from ±4% to a smaller value, providing a more precise estimate.

c. External validity would not necessarily become less important. External validity refers to the generalizability of the findings to the broader population. Increasing the sample size alone does not directly affect external validity, which depends more on the sampling method and the representativeness of the sample.

d. Statistical validity would not become negatively affected. A larger sample size generally improves statistical validity by increasing the power of the study to detect significant effects or relationships. With a larger sample size, the study is less likely to commit a Type II error (failing to reject a false null hypothesis).