100% Statistical Inferences Quiz

A simple random sample is drawn from a normally distributed population. The value of which of the following will not be known for certain but can be inferred?

A

A simple random sample is drawn from a normally distributed population, and when making a statistical inference about the population mean, the margin of error is found to be 5.9 at a 95% level of confidence. If the mean of the sample is 18.7, what is the 95% confidence interval for the population mean?

A. 18.7 ± 5.9

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?

B. No, because she did not use a simple random sample.

All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn?

B. The margin of error is multiplied by srt root 2.

Which of the following z-values, standard deviations, and sample sizes produce a margin of error of 0.95?

B. z = 2.14; s = 4; n = 81

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probability, assuming a confidence level of 86%?

C. 0.93

Suppose the mean of a normally distributed population is 300, and 200 simple random samples are drawn from the population. At a 68% confidence level, (one standard deviation from the mean), about how many of the samples' confidence intervals would you expect to contain the population mean?

C. 136

The times it took for 35 loggerhead sea turtle eggs to hatch in a simple random sample are normally distributed, with a mean of 50 days and a standard deviation of 2 days. Assuming a 95% confidence level (95% confidence level = z-score of 1.96), what is the margin of error for the population mean?

D. 0.66

Which of the following statements is correct?

D. Sample statistics are used to make inferences about population parameters.

Jason and Yolanda both drew a simple random sample from a non-normally distributed population of 25,000. Jason's sample consisted of 0.24% of the population, while Yolanda's sample consisted of 0.32% of the population. Whose sample can be used to make inferences about the population?

D. both Jason's sample and Yolanda's sample