Question

Which one of the following statements is true regarding two random samples, drawn in the same way, from the same population, one of size 30 and one of size 300?

1) The two samples are expected to have the same sample mean.
2) The larger sample is more likely to produce a large sample mean.
3) The smaller sample will have a smaller 95% confidence interval for the population mean.
4) The smaller sample will, on average, produce a lower estimate of the variance of the population.

Answer 1

The smaller sample will have a smaller 95% confidence interval for the population mean.

Step-by-step explanation:

The statement that is true regarding two random samples, drawn in the same way, from the same population, one of size 30 and one of size 300 is: 3) The smaller sample will have a smaller 95% confidence interval for the population mean.

When calculating a confidence interval for the population mean, a larger sample size will result in a smaller margin of error and a narrower confidence interval. Since the sample size of 300 is larger than the sample size of 30, the confidence interval for the population mean will be smaller for the smaller sample.