Yvon Hopps ran an experiment to determine optimum power and time settings for microwave popcorn. His goal was to find a combination of power and time that would deliver high-quality popcorn with less than 10% of the kernels left un-popped, on average. After experimenting with several bags, he determined that power 9 at 4 minutes was the best combination. To be sure that the method was successful, he popped 8 more bags of popcorn (selected at random) at this setting. All were of high quality, with the following percentages of uncooked popcorn: 7, 13.2, 10, 6, 7.8, 2.8, 2.2, and 5.2. Does the 95% confidence interval suggest that he met his goal of an average of no more than 10% uncooked kernels? Explain.

The company contacts 620 people selected at random and only 157 remember the ad.

Should the company renew the contract? Support your recommendation with an appropriate test.

After the political ad campaign described, pollsters check the governor's negatives. They test the hypothesis that the ads produced no change against the alternative that the negatives are now below 30% and find a P-value of 0.22. Which conclusion is appropriate? Explain. a) There's a 22% chance that the ads worked. b) There's a 78% chance that the ads worked. c) There's a 22% chance that their poll is correct. d) There's a 22% chance that natural sampling variation could produce poll results like these if there's really no change in public opinion.

A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has certified as okay. They will revoke the shop's license if they find significant evidence that the shop is certifying vehicles that do not meet standards. In this context, what is a Type I error?

A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. Given the histogram.

A computer program found that the resulting 95% confidence interval for the mean amount spent in March 2011 is (-$28,366.84,$90,691.49). Explain why the analysts didn't find the confidence interval useful, and explain what went wrong.

A medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following Student 's t-based confidence interval:

$$\left. \begin{array} { c } { \text { With } 95.00 \% \text { Confidence, } } \\ { 70.887604 < \mu ( \text { Pulse } ) < 74.497011 } \end{array} \right.$$

If the researcher had calculated a 99% confidence interval, would the margin of error be larger or smaller? Explain.

A medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following Student 's t-based confidence interval:

$$\left. \begin{array} { c } { \text { With } 95.00 \% \text { Confidence, } } \\ { 70.887604 < \mu ( \text { Pulse } ) < 74.497011 } \end{array} \right.$$

Explain carefully what the software output means.

The LSAT (a test taken for law school admission) has a mean score of 151 with a standard deviation of 9 and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of 9 students at a time. A larger organization teaches classes of 25 students at a time. Both organizations publish the mean scores of all their classes. If either organization has a graduating class with a mean score of 160, they'll take out a full-page ad in the local school paper to advertise. Which organization is more likely to have that success? Explain.

If you test a hypothesis and reject the null hypothesis in favor of the alternative hypothesis, does your test prove that the alternative hypothesis is correct? Explain.

What does a $90\%$ confidence interval mean?

What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are summary statistics for the percentage of flights departing on time each month from 1995 through September 2011.

There is no evidence of a trend over time. (The correlation of On Time Departure% with time is $r=-0.016$.)

c) Interpret this interval for a traveler planning to fly.

What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are summary statistics for the percentage of flights departing on time each month from 1995 through September 2011.

There is no evidence of a trend over time. (The correlation of On Time Departure% with time is $r=-0.016$.)

a) Check the assumptions and conditions for inference.

The Paralyzed Veterans of America is a philanthropic organization that relies on contributions. They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution. To test a new campaign, they recently sent letters to a random sample of 100,000 potential donors and received 4781 donations.

In the earlier exercise from the previous chapter, we saw an ogive of the distribution of cholesterol levels (in mg/dL) of a random sample of 1406 participants (taken in 1948 from Framingham, MA). To find a bootstrap confidence interval for the mean cholesterol, a student took 1000 bootstrap samples, calculated the mean of each, and given the figure of the histogram of the bootstrap means:

Summary statistics of the means show:

$$\begin{array}{cccccccccc} 0.5 \% & 1 \% & 2 \% & 2.5 \% & 5 \% & 95 \% & 97.5 \% & 98 \% & 99 \% & 99.5 \% \\ 231.890 & 232.130 & 232.370 & 232.434 & 232.769 & 236.763 & 237.130 & 237.281 & 237.526 & 237.873 \end{array}$$

Interpret the 95% confidence interval for the mean cholesterol.