7. Sampling Distributions & Confidence Intervals: Mean

For a two-tailed hypothesis test using a 5% significance level, what is the critical value of $z$?

According to the law of large numbers, as the sample size increases, which of the following statements is true about the $\mathrm{sample mean}$?

Which of the following formulas correctly calculates the standard error of the mean for a data set with sample standard deviation $s$ and sample size $n$?

Which of the following would not cast doubt on the usefulness of sample data in constructing a confidence interval?

Suppose the waiting times for patients needing emergency service are normally distributed with a mean of $\mu =12$ minutes and a standard deviation of $\sigma =3$ minutes. What proportion of patients wait $9$ minutes or less?

In the context of hypothesis testing, which of the following gives the probability of making a Type I error?

Which of the following best describes what the Central Limit Theorem states in the context of confidence intervals?

Make a 90% confidence interval for a parameter, y, with point estimate $ŷ=-1.5$, & margin of error $E=3.25$.

Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics.

c = 0.98

Find the critical value, $z_{\frac{\alpha }{2}}$, for a 80% 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?

Given a time-series trend equation of $25.3+2.1x$, what is the forecasted value for period $7$?

Which of the following is not a characteristic of the distribution of sample means?

Based on the bar chart showing the $95\%$ confidence intervals for the mean test scores of four different classes, which of the following is an accurate conclusion?

Estimating the Median Use the sample data listed in Exercise 1 “Bootstrap Requirements” to generate 1000 bootstrap samples, and find the median in each of those samples. After obtaining the 1000 sample medians, find the 95% confidence interval estimate of the population median by evaluating p2.5 and p97.5 from the sorted 1000 medians. Given that the sample times in Exercise 1 are from the 50 times in Data Set 20 “Alcohol and Tobacco in Movies” and those 50 times have a median of 5.5, how well did the bootstrap method work to create a “good” confidence interval?