7. Sampling Distributions & Confidence Intervals: Mean

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.

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 $\mu =x_1-x_2$?

To study the concentration of a particular pollutant (in parts per million) in a local river, an environmental scientist collects 32 water samples from random locations. They get $\bar{x}=3.87$ ppm & know from previous data that $\sigma =0.62$ ppm. Make a 99% conf. int. for the mean pollutant concentration.

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)?

Fill out the table using a calculator and $n=30$.

Find the critical value $t_{\frac{\alpha }{2}}$for an 80% confidence interval given a sample size of 51.

A technician wants to estimate the average battery life of a new type of smart phone, so he tests 8 randomly selected phones & records the data below. Assuming battery life has a normal dist, make a 90% conf. int. for the mean battery life.

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.