In Exercises 1–4, refer to the accompanying screen display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used.

Interpreting a Confidence Interval The results in the screen display are based on a 95% confidence level. Write a statement that correctly interprets the confidence interval.

In Exercises 1–4, refer to the accompanying screen display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used.

Degrees of Freedom

a. What is the number of degrees of freedom that should be used for finding the critical value ta/2?

In Exercises 1–4, refer to the accompanying screen display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used.

Degrees of Freedom

b. Find the critical value ta/2 corresponding to a 95% confidence level.

Second-Hand Smoke Refer to Data Set 15 “Passive and Active Smoke” and construct a 95% confidence interval estimates of the mean cotinine level in each of three samples: (1) people who smoke; (2) people who don’t smoke but are exposed to tobacco smoke at home or work; (3) people who don’t smoke and are not exposed to smoke. Measuring cotinine in people’s blood is the most reliable way to determine exposure to nicotine. What do the confidence intervals suggest about the effects of smoking and second-hand smoke?

In Exercises 5–8, (a) identify the critical value ta/2 used for finding the margin of error, (b) find the margin of error, (c) find the confidence interval estimate of u, and (d) write a brief statement that interprets the confidence interval.

Birth Weights Here are summary statistics for randomly selected weights of newborn girls: n=36, x=3150.0g, s=695.5g (based on Data Set 6 “Births” in Appendix B). Use a confidence level of 95%.

Mean IQ of Data Scientists See the preceding exercise, in which we can assume that sigma=15 for the IQ scores. Data scientists are a group with IQ scores that vary less than the IQ scores of the general population. Find the sample size needed to estimate the mean IQ of data scientists, given that we want 98% confidence that the sample mean is within 2 IQ points of the population mean. Does the sample size appear to be practical?

In Exercises 1–4, refer to the accompanying screen display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used.

Refer to the accompanying screen display.

a. Express the confidence interval in the format that uses the “less than” symbol. Round the confidence interval limits given that the original times are all rounded to one decimal place.