7. Sampling Distributions & Confidence Intervals: Mean

Which of the following is a point estimate for the population mean $\mu$?

Which of the following calculations is not derived from the confidence interval for a population mean $\mu$?

In the context of confidence intervals for a population mean, what happens to the expected value of the sample mean $m$ as the sample size increases?

When using the Student's $t$ distribution to construct a confidence interval for the population mean, which of the following conditions must be met?

Suppose you are constructing a conditional relative frequency table by column for a survey of students' favorite subjects. If the relative frequencies in one column are $0.17$, $0.25$, and $x$, and the sum of the column must be $1$, which value for $x$ completes the table?

When constructing a $90\%$ confidence interval for the population mean with a sample size of $n=50$, which constant should be used as the critical value if the population standard deviation is known?

If the significance level $\alpha$ is $0.10$, what is the corresponding confidence level for a confidence interval for the population mean?

When drawing independent random samples from two normal populations, what is the distribution of the difference between the sample means $\mu =x_1-x_2$?

A properly drawn random sample of one thousand individuals is used to estimate a population mean. The sampling error for the sample mean is roughly plus or minus what percent of the population mean (assuming a normal distribution and no prior knowledge of population standard deviation)?

The data set represents the scores of 12 randomly selected students on the SAT Physics Subject Test. Assume the population test scores are normally distributed and the population standard deviation is 108. (Adapted from The College Board)

b. Construct a 90% confidence interval for the population mean. Interpret the results.

Use the standard normal distribution or the t-distribution to construct the indicated confidence interval for the population mean of each data set. Justify your decision. If neither distribution can be used, explain why. Interpret the results.

a. In a random sample of 40 patients, the mean waiting time at a dentist’s office was 20 minutes and the standard deviation was 7.5 minutes. Construct a 95% confidence interval for the population mean.

In the context of confidence intervals for population mean, an interval estimate is used to estimate $\_\_\_\_\_$.

Gas prices are getting more and more expensive. The average gas price, from a random sample of 100 gas stations, was \$3.50. It is assumed that gas prices have a standard deviation of \$0.04. Construct an 80% confidence interval for the true mean gas price in the United States.

Books get more and more expensive every semester, but the distribution of their prices is always normal. 25 randomly selected students in your school spent, on average \$500 with a standard deviation of \$50. Construct a 98% confidence interval for the true spending on books.

You want to purchase one of the new Altima. You randomly select 400 dealerships across the United States and find a mean of \$25,000. Assume a population standard deviation of \$2500. Construct and interpret a 94% confidence interval for the true mean price for the new Nissan Altima.