7. Sampling Distributions & Confidence Intervals: Mean

Which of the following correctly compares the $t$-distribution and $z$-distribution?

For a specific confidence level, what happens to the width of a confidence interval for the mean as the sample size increases (assuming population standard deviation is known)? The confidence interval for the mean is typically given by $\mu \pm z\bullet \frac{\sigma }{\sqrt{n}}$, where $n$ is the sample size.

Which of the following is the correct critical value $z*$ for a confidence level of $70\%$ in a standard normal distribution?

In the context of repeated-measures designs, what value is estimated by constructing a confidence interval using the repeated-measures $t$ statistic?

In the context of the widget cost regression model, what does the $p$-value associated with the $F$ statistic indicate?

Which of the following is not true of the confidence level of a confidence interval?

Suppose a $95\%$ confidence interval for the mean difference in blood pressure between a treatment group and a control group is $(-2,5)$. Based on this interval, what does the confidence interval suggest about the effectiveness of the treatment?

In the context of interpreting a graph related to confidence intervals, why might the $\mathrm{percentages}$ shown not add up to $100\%$?

Which of the following correctly expresses a confidence interval for a population mean in the standard form?

By the empirical rule, how many students in a class of $200$ would score within the range $\mu \pm 2\sigma$?

In order to make statistical inferences when testing a population mean, which of the following conditions must typically be met?

Suppose a $95\%$ confidence interval for the average age of all celebrities is calculated from a sample. What does this confidence interval tell us about the population of all celebrities?

Which of the following is true about research based on a sample?

Which of the following statements about the $standarderror$ of the estimate is true?

What is the primary purpose of statistical inference in the context of $confidence intervals$?