7. Sampling Distributions & Confidence Intervals: Mean

Suppose you have a random sample of $50$ measurements with a sample mean of $20$ and a known population standard deviation of $4$. You want to construct a $95\%$ confidence interval for the population mean. Which of the following is a correct analysis of this data set?

Which of the following is important to ensure that a study has statistical validity?

All else being equal, which of the following methods can help increase the power of a study?

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?

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?

Which of the following is not a conclusion of the Central Limit Theorem?