3.Which statement is correct regarding a confidence interval for the mean?

• A confidence interval is used to estimate a likely value for asample mean.
• A confidence interval is used to estimate a likely value for the standard deviation.
• A confidence interval is used to show the probability of the null hypothesis being true.
• A confidence interval isused to approximate a likely value for the population mean.

4.You want to figure out if the amount of sleep you get at night helps increase the grade you get on an exam the following day.You decide to record how many hours of sleep you and your friends got before an exam along with the grade you received on that exam. You then plot the results on a scatterplot and find that as the number of hours of sleep goes up, so do the exam grades. You then conclude that increased sleep causes higher exam scores.

Is your conclusion necessarily true?

• No, because the apparent correlation between sleep and exam scores might be caused by another variable.
• No, because the number of hours of sleep and exam scores are not necessarily correlated.
• Yes, because sleep and exam scores are highly correlated.
• Yes, because as the number of hours of sleep increases, so do exam scores.