7. Sampling Distributions & Confidence Intervals: Mean

Which of the following best describes the meaning of a $99\%$ confidence interval for a population mean?

In the context of confidence intervals, what does the margin of error account for?

Which concept below is not a main idea of estimating a population proportion?

Which of the following best describes the interpretation of a $96\%$ confidence level in the context of confidence intervals?

Distributions Identify the distribution (normal, Student t, chi-square) that should be used in each of the following situations. If none of the three distributions can be used, what other method could be used?

a. In constructing a confidence interval of , you have 75 sample values and they appear to be from a population with a skewed distribution. The population standard deviation is not known.

Arm Circumferences Listed below are arm circumferences (cm) of randomly selected women (based on Data Set 1 “Body Data” from Appendix B). Also shown is the normal quantile plot of those measurements.

b. Are the requirements for constructing a 95% confidence interval estimate of the population standard deviation satisfied? If so, construct that confidence interval.

Which of the following best describes the main disadvantage of the moving average when used to estimate a population parameter in the context of confidence intervals?

In the context of confidence intervals, if Figure 7-7 shows 'line a' representing the range within which a population parameter is expected to fall with a certain level of confidence, what type of statistical forecasting does 'line a' most likely depict?

Based on the statistical model you developed, which of the following statements about confidence intervals is true?

In Exercises 1–4, a population has a mean mu and a standard deviation sigma. Find the mean and standard deviation of the sampling distribution of sample means with sample size n.

Mu = 1275, sigma =6, n = 1000

Which of the following is not a time-series model?

True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

As the sample size increases, the standard deviation of the distribution of sample means increases.

Pulse Rates of Women and Men Using the samples of women and men included in Data Set 1 “Body Data,” we get this 95% confidence interval estimate of the difference between the population mean of pulse rates (bpm) of women and the population mean of pulse rates (bpm) of men: 1.7 bpm < u1-u2 < 7.2bpm. In this confidence interval, women correspond to population 1 and men correspond to population 2.

a. What does the confidence interval suggest about equality of the mean pulse rate of women and the mean pulse rate of men?

Interpreting Normal Quantile Plots. In Exercises 5–8, examine the normal quantile plot and determine whether the sample data appear to be from a population with a normal distribution.

Ages of Presidents The normal quantile plot represents the ages of presidents of the United States at the times of their inaugurations. The data are from Data Set 22 “Presidents” in Appendix B.

In the context of constructing a confidence interval for the mean of a normal distribution with known variance, which function is used to evaluate the probability that a sample mean falls within a certain range of the population mean?