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For each of the following hypothesis testing scenarios, indicate whether or not the appropriate hypothesis test would be for a difference in two population means. If not, explain why not.

Many runners believe that listening to music while running enhances their performance. The authors of the paper "Effects of Synchronous Music on Treadmill Running Among Elite Triathletes" (Journal of Science and Medicine in Sport \([2012]: 52-57)\) wondered if this is true for experienced runners. They recorded time to exhaustion for 11 triathletes while running on a treadmill at a speed determined to be near their peak running velocity. The time to exhaustion was recorded for each participant on two different days. On one day, each participant ran while listening to music that the runner selected as motivational. On a different day, each participant ran with no music playing. For purposes of this exercise, assume that it is reasonable to regard these 11 triathletes as representative of the population of experienced triathletes. Only summary quantities were given in the paper, but the data in the table on the next page are consistent with the means and standard deviations given in the paper. Do the data provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music? Test the relevant hypotheses using a significance level of \(\alpha=0.05\).

To determine if chocolate milk is as effective as other carbohydrate replacement drinks, nine male cyclists performed an intense workout followed by a drink and a rest period. At the end of the rest period, each cyclist performed an endurance trial in which he exercised until exhausted, and the time to exhaustion was measured. Each cyclist completed the entire regimen on two different days. On one day, the drink provided was chocolate milk, and on the other day the drink provided was a carbohydrate replacement drink. Data consistent with summary quantities in the paper "The Efficacy of Chocolate Milk as a Recovery Aid" (Medicine and Science in Sports and Exercise [2004]: S126) are given in the table at the bottom of the page. Is there evidence that the mean time to exhaustion is greater after chocolate milk than after a carbohydrate replacement drink? Use a significance level of \(\alpha=0.05\).

In the study described in the paper "Exposure to Diesel Exhaust Induces Changes in EEG in Human Volunteers" (Particle and Fibre Toxicology [2007]), 10 healthy men were exposed to diesel exhaust for 1 hour. A measure of brain activity (called median power frequency, or MPF in Hz) was recorded at two different locations in the brain both before and after the diesel exhaust exposure. The resulting data are given in the accompanying table. For purposes of this exercise, assume that the sample of 10 men is representative of healthy adult males. Construct and interpret a \(90 \%\) confidence interval estimate for the difference in mean MPF at brain location 1 before and after exposure to diesel exhaust.

Breast feeding sometimes results in a temporary loss of bone mass as calcium is depleted in the mother's body to provide for milk production. The paper "Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with Low Calcium Intakes" (American Journal of Clinical Nutrition [2004]: 1322-1326) gave the accompanying data on total body bone mineral content (in grams) for a representative sample of mothers both during breast feeding (B) and in the post-weaning period (P). Use a \(95 \%\) confidence interval to estimate the difference in mean total body bone mineral content during post- weaning and during breast feeding.

The uuthors ol the paper "Concordance of Self-Report and Measured Height and Weight of College Students" (Journal of Nutrition, Education and Behavior [2015]: \(94-98\) ) used a pairedsamples \(t\) test to reach the conclusion that male college students tend to over-report both weight and height. This conclusion was based on a sample of 634 male college students selected from eight different universities. The sample mean difference between the reported weight and actual measured weight was 1.2 pounds and the standard deviation of the differences was 5.71 pounds. For purposes of this exercise, you can assume that the sample was representative of male college students. a. Carry out a hypothesis test to determine if there is a significant difference in the mean reported weight and the mean actual weight for male college students. b. For height, the mean difference between the reported height and actual measured height was 0.6 inches and the standard deviation of the differences was 0.8 inches. Carry out a hypothesis test to determine if there is a significant difference in the mean reported height and the mean actual height for male college students. c. Do the conclusions reached in the hypothesis tests of Parts (a) and (b) support the given conclusion that male college students tend to over-report both height and weight? Explain.

The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits ("2013 International Bedroom Poll Summary of Findings," www.sleepfoundation.org/sites /default/files/RPT495a.pdf, retrieved May 20,2017 ). Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night. For the United States, the sample mean was 391 minutes, and for Mexico the sample mean was 426 minutes. Suppose that the sample standard deviations were 30 minutes for the U.S. sample and 40 minutes for the Mexico sample. The report concludes that on average, adults in the United States get less sleep on work nights than adults in Mexico. Is this a reasonable conclusion? Support your answer with an appropriate hypothesis test.

The article "Plugged \(\mathrm{In}\), but Tuned Out" (USA TODAY, January 20,2010 ) summarizes data from two surveys of kids age 8 to 18. One survey was conducted in 1999 and the other was conducted in \(2009 .\) Data on number of hours per day spent using electronic media, consistent with summary quantities in the article, are given (the actual sample sizes for the two surveys were much larger). For purposes of this exercise, you can assume that the two samples are representative of kids age 8 to 18 in each of the 2 years when the surveys were conducted. $$ \begin{array}{rrrrrrrrrrrrr} \mathbf{2 0 0 9} & 5 & 9 & 5 & 8 & 7 & 6 & 7 & 9 & 7 & 9 & 6 & 9 \\ & 10 & 9 & 8 & & & & & & & & & \\ \mathbf{1 9 9 9} & 4 & 5 & 7 & 7 & 5 & 7 & 5 & 6 & 5 & 6 & 7 & 8 \\ & 5 & 6 & 6 & & & & & & & & & \end{array} $$ a. Because the given sample sizes are small, what assumption must be made about the distributions of electronic media use times for the two-sample \(t\) test to be appropriate? Use the given data to construct graphical displays that would be useful in determining whether this assumption is reasonable. Do you think it is reasonable to use these data to carry out a two-sample \(t\) test? b. Do the given data provide convincing evidence that the mean number of hours per day spent using electronic media was greater in 2009 than in \(1999 ?\) Test the relevant hypotheses using a significance level of \(\alpha=0.01\).

What impact does fast-food consumption have on various dietary and health characteristics? The article "Effects of Fast-Food Consumption on Energy Intake and Diet Quality among Children in a National Household Study" (Pediatrics, 2004: \(112-118\) ) reported the accompanying summary statistics on daily calorie intake for a representative sample of teens who do not typically eat fast food and a representative sample of teens who do eat fast food. Is there convincing evidence that the mean calorie intake for teens who typically eat fast food is greater than the mean intake for those who don't by more than 200 calories per day?

A researcher at the Medical College of Virginia conducted a study of 60 randomly selected male soccer players and concluded that players who frequently "head" the ball have a lower mean IQ than those who do not (USA TODAY, August 14,1995 ). The soccer players were divided into two groups, based on whether they averaged 10 or more headers per game. Mean IQs were reported in the article, but the sample sizes and standard deviations were not given. Suppose that these values were as given in the accompanying table. Do these data support the researcher's conclusion? Test the relevant hypotheses using \(\alpha=0.05 .\) Can you conclude that heading the ball causes lower IQ? Explain.