Question

the number of sit-ups that all tenth-grade girls can do in 5 minutes is normally distributed. beth surveyed 20 of her fellow intramural tennis players, all tenth-grade girls, and determined the mean number of sit-ups they could do. can she make an inference about the population mean for all tenth-grade girls based on the sample?

no, because the sample size was not big enough.
no, because she did not use a simple random sample.
yes, because the sample size was big enough.
yes, because she used a simple random sample.

Explanation:

Identify the population and sample

The target population is "all tenth-grade girls." The sample consists of "20 of her fellow intramural tennis players, all tenth-grade girls."

Analyze the sampling method

Using the Convenience Sampling knowledge point, Beth selected a sample that was easy to reach (her tennis teammates) rather than using a random selection process. This group is not representative of all tenth-grade girls, as athletic tennis players may have different physical fitness levels compared to the general population.

Evaluate the validity of inference

Using the Sampling Bias Sources knowledge point, because the sample is biased and non-random, she cannot generalize her findings to make a valid statistical inference about the entire population mean. A simple random sample is required to avoid selection bias and ensure every member of the population has an equal chance of being selected.

Match with the correct option

The correct option must state that she cannot make the inference because she did not use a simple random sample. This corresponds to the second option.

Answer:

• No, because the sample size was not big enough.
• No, because she did not use a simple random sample. (Correct answer)
• Yes, because the sample size was big enough.
• Yes, because she used a simple random sample.