A survey was done of men’s and women’s hands to see if the ring finger appeared longer than the index finger or not. Yes means the ring finger is longer, and No means the ring finger appears shorter or the same length as the index finger. The students in this survey were not told the theory that men are more likely to have a longer ring finger than women due to more testosterone.

	Men	Women
Yes	33	32
No	7	13

a. What percentage of the men said Yes?
b. What percentage of the women said Yes?
c. What percentage of the people who said Yes were men?
d. If a large group of $250$ men had the same rate of responses as the men in this sample, how many men of the $250$ would say yes?

Read the passage. Then answer the question. If you rinse greasy hands in water, the grease does not wash off because the molecules of the compounds in grease are nonpolar, while the molecules of water are polar. If you use soap, though, the grease washes away. The molecules of soap are long chains of atoms with a polar end and a nonpolar end. The nonpolar ends surround grease molecules, dissolving them. Then the polar ends of the soap molecules interact with water to make the whole group soluble in water. When the polar end of soap reacts with calcium ions, it forms a salt that is not very soluble in water. How does this explain the observation that soap does not work well in hard water, which contains dissolved calcium ions?

An article in the British medical journal The Lancet claimed that autism was caused by the measles, mumps, and rubella (MMR) vaccine (Wakefield et al. 1998). This vaccine is typically given to children twice, at about the age of 1 and again at about 4 years of age. The article reports a study of 12 children with autism who had all received the vaccines shortly before developing autism. The article was later retracted by The Lancet because the conclusions were not justified by the design of the study.

Explain why The Lancet might have felt that the conclusions were not justified by listing potential flaws in the study, as described earlier.

A sample of students were questioned to determine how much they would be willing to pay to see a movie in a theater that served dinner at the seats.

The male students responded (in dollars): 10, 15, 15, 25, and 12.

The female students responded: 8, 30, 15, and 15.

Write these data as they might appear in

(a) stacked format with codes

(b) unstacked format

Emmanuel, a student at a Los Angeles high school, kept track of the calorie content of all the snacks he ate for one week. He also took note of whether the snack was mostly “sweet” or “salty.”

The sweet snacks: 90, 310, 500, 500, 600, 90

The salty snacks: 150, 600, 500, 550

Write these data as they might appear in

(a) stacked format with codes

(b) unstacked format.

The Harvard Heart Letter reported on a study that examined the diets of $1226$ older women over $15$ years. They discovered that the more vegetables the women consumed, the lower their risk of dying of cardiovascular disease. From this study can we conclude that eating a diet high in vegetables prevents cardiovascular disease? Why or why not?

You can find many testimonials on the Internet that drinking aloe vera juice helps with digestive ailments. From these testimonials can we conclude that aloe vera juice causes digestive problems to go away? Why or why not?

The blog NHS Choices (February 10, 2014) noted that “there has been increasing anecdotal evidence that vitamin C may still be useful as an anticancer medicine if used in high concentrations and given directly into the vein (intravenously).” Explain what it means that there is “increasing anecdotal evidence” that Vitamin C may be a useful anticancer medicine. How does anecdotal evidence contrast with scientific evidence? What kind of conclusions, if any, can be made from anecdotal evidence?

The data in the given table were collected from one of the authors’ statistics classes. The first row gives the variable, and each of the other rows represents a student in the class:

Suppose you wanted to know whether the men or the women tended to be taller. Could you do that with this data table? If so, which variables would you use?

A study was conducted to see whether participants would ignore a sign that said, “Elevator may stick between floors. Use the stairs.” The study was done at a university dorm on the ground floor of a three-level building. Those who used the stairs were said to be compliant, and those who used the elevator were said to be noncompliant. There were three possible situations, two of which involved confederates. A confederate is a person who is secretly working with the experimenter. In the first situation, there was no confederate. In the second situation, there was a compliant confederate (one who used the stairs), and in the third situation, there was a noncompliant confederate (one who used the elevator). The subjects tended to imitate the confederates. What more do you need to know about the study to determine whether the presence or absence of a confederate causes a change in the compliance of subjects?

The accompanying table gives the population (in hundred thousands) and number of people not covered by health insurance (in hundred thousands) for the United States. Find the percentage of people not covered by health insurance for each of the given years and describe the trend. (Source: 2017 World Almanac and Book of Facts)

Designing a Plumb Bob Having been asked to design a brass plumb bob that will weigh in the neighborhood of 190 g, you decide to shape it like the solid of revolution shown here.

(b) If you specify a brass that weighs $8.5 \mathrm{~g} / \mathrm{cm}^3$, how much will the plumb bob weigh to the nearest gram?

What is the difference between a categorical variable and a numerical variable?.

The weights of four randomly chosen bags of horse carrots, each bag labeled 20 pounds, were 20.5, 19.8, 20.8, and 20.0 pounds. Assume that the distribution of weights is Normal. Find a 95-percentage confidence interval for the mean weight of all bags of horse carrots. Use technology for your calculations.

a. Decide whether each of the following three statements is a correctly worded interpretation of the confidence interval, and fill in the blanks for the correct option(s).

i. 95 percentage of all sample means based on samples of the same size will be between ___ and ___.

ii. I am 95 percentage confident that the population mean is between ___ and ___.

iii. We are 95 percentage confident that the boundaries are ___ and ___.

b. Can you reject a population mean of 20 pounds? Explain.