AP Stats Exam 4

A program that was intended to cure a person’s fear of spiders was offered at a local zoo. Volunteers with a fear of spiders participated in the program, which included holding a spider for 15 minutes. One month after they completed the program, the participants were contacted and surveyed about the program. Over 90 percent of the participants claimed that they were cured of their fear of spiders. Based on the description of the program, which of the following statements is true?

• Because over 90% of the participants claimed to be cured, the results prove that holding a spider will cure a person’s fear of spiders.

• Because over 90% of the participants claimed to be cured, the results can be generalized to the population of all people who have a fear of spiders.

• Because the participants were volunteers, the study is a census of all people in the local area who have a fear of spiders.

• Because the participants are self-selected, a person’s desire to be cured could be a confounding variable.

• Because participants held a spider for 15 minutes, the study is an experiment and the results can be generalized to the population of all people who have a fear of spiders.

A study was conducted to evaluate the impact of taking a nutritional supplement on a person’s reaction time. One hundred volunteers were placed into one of three groups according to their athletic ability: low, moderate, or high. Participants in each group were randomly assigned to take either the nutritional supplement or a placebo for six weeks. At the end of the six weeks, participants were given a coordination task. The reaction time for completing the task was recorded for each participant. The study compared the reaction times between those taking the supplement and those taking the placebo within each athletic ability level. Which of the following is the best description of the study?

• A randomized block design

• A completely randomized design

• A matched-pairs design

• A randomized observational study

• A stratified observational study.

An agricultural scientist wanted to compare the effect of a new fertilizer to that of three older fertilizers—X, Y, and Z—on the growth of vegetables typically grown in small gardens. Two hundred green been seedlings were individually planted in identical pots and randomly assigned to one of four groups of 50 each. Seedlings in one group were given the new fertilizer, and the three remaining groups of seedlings were given fertilizers X, Y or Z, respectively. At the end of four weeks, all seedlings were dried and weighed. The scientist found that the mean weight of the seedlings in the group given the fertilizer was significantly greater than the mean weights of seedlings in the other three groups. The scientists concluded that the new fertilizer was more effective than the other fertilizers for all vegetables. Why is the scientist’s conclusion not appropriate?

• The study was observational, so cause and effect cannot be concluded.

• The study was observational, so no replication was used in the study.

• The experiment only included green beans, so the results cannot be generalized to all vegetables.

• The experiment did not group the seedlings into blocks by the variety of beans.

• The experiment lacked a control group that did not use any fertilizer.

In one region of the country, the mean length of stay in hospitals is 5.5 days with a standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with a mean length of stay,  $\overline{x}$   , recorded for each sample. Which of the following is the best description of the sampling distribution of  $\overline{x}$  ?

• Strongly skewed to the right with mean 5.5 and standard deviation 2.6 days.

• Strongly skewed to the right with mean 5.5 and standard deviation .26 day.

• Strongly skewed to the right with mean 5.5 days and standard deviation .026 day.

• Approximately normal with mean 5.5 days and standard deviation 2.6 days.

• Approximately normal with mean 5.5 days and standard deviation .26 day.

A local television news station includes a viewer survey question about current issue at the beginning of every evening news broadcast. Viewers are invited to use social media to respond to the question. The result of the survey are shared with the audience at the end of each broadcast. In relation to the opinions of the population of the region, which of the following is a possible reason why the result of such surveys could be biased?

I. Viewers with strong opinions about the current issue are more likely to respond than are viewers without strong opinions.

II. The opinions of viewers of one television station are not necessarily representative of the population of a region.

III. Viewers with access to social media are not necessarily representative of the population of a region.

• I only

• II only

• III only

• II and III only

• I, II, and II

Researchers wanted to investigate whether babies have a sense of right and wrong. They showed each of 60 babies a puppet show in which a red puppet was trying to open a heavy box lid. A second puppet, called the helper, would try to help the red puppet open the box, while a third puppet, called the hinderer, would try to slam the box lid down. After watching the show, each baby was presented with a tray containing the helper puppet and the hinderer puppet, and the researchers recorded which puppet the baby reached for. The researchers wanted to determine whether the babies would reach for the helper puppet more than for the hinderer puppet.

As part of the show, a green puppet and a yellow puppet served as the helper and the hinderer. For each baby, a coin was tossed to determine which color would serve which role. Which of the following is the most important reason for the random assignment of color to role in the study?

• Slamming the lid might cause war on the hinderer puppet after 60 shows. The random assignment of color to role permits more even wear between the helper and the hinderer.

• The puppeteer might grow tired of doing the same show with the same puppet colors. Random assignment of color to role keeps the show fresh for each performance.

• If the same role is played by the same color puppet, the babies might show a preference for the color instead of a preference for the role.

• The random assignment of color to role allows the researchers to determine if one color is better than another in teaching babies right from wrong.

• Boys and girls prefer different colors. The random assignment of color to role ensures that the show is equally accessible to boys and girls.

Some contact lens wearers report problems with dryness in their eyes. A study was conducted to evaluate the effectiveness of new eye-drop solution to relieve dryness for contact lens wearers. Twenty-five volunteers who wore contact lenses agreed to use the new solution for one month. At the end of the month, 36 percent of the volunteers reported that the new solution was effective in relieving dryness. The company that produced the new eye-drop solution concluded that using the new solution is more effective in relieving dryness than using no solution. Which of the following best explains why the study does not support such a conclusion?

• The sample size was too small.

• The study had no control group

• The participants were volunteers.

• The participants self-reported the frequency with which they used the new solution.

• The participants self-reported the effectiveness of the new solution.

A simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6, respectively. All 10 dice were rolled, and the average of the 10 numbers appearing face-up was recorded. The process was repeated 20 times. Which of the following best describes the distribution being simulated?

• A sampling distribution of a sample mean with  $n=10$  ,  $\mu_{\overline{x}}=3.5$  , and  $\sigma_{\overline{x}}\approx0.54$  

• A sampling distribution of a sample mean with  $n=10$  ,  $\mu_{\overline{x}}=3.5$  , and  $\sigma_{\overline{x}}\approx1.71$  

• A sampling distribution of a sample mean with  $n=20$  ,  $\mu_{\overline{x}}=3.5$  , and  $\sigma_{\overline{x}}\approx0.38$  

• A sampling distribution of a sample proportion with  $n=10$  ,  $\mu_{phat}=\frac{1}{6}$  , and  $\sigma_{phat}\approx0.118$  

• A sampling distribution of a sample proportion with  $n=20$  ,  $\mu_{phat}=\frac{1}{6}$  , and  $\sigma_{phat}\approx0.083$  

A researcher wanted to estimate the average amount of money spent on extracurricular activities per school in a certain region. The researcher randomly selected 20 public schools and 20 private schools in the region to use for a sample, which of the following best describes the type of sample that was taken?

• A census

• A cluster sample

• A convenience sample

• A simple random sample

• A stratified random sample

Which of the following pairs of sample size n and the population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p-hat?

• n=1,000 and p close to 0.

• n=1,000 and p close to 1.

• n=1,000 and p close to 12.

• n=100 and p close to 0.

• n=100 and p close to 12.