AP Statistics Review #4

The probability that a softball player gets a hit in any single at-bat is 0.300. Assuming that the player's chance of getting a hit during a particular time at bat is independent of the player's other times at bat, what is the probability that the player will not get a hit until their fourth time at bat?

In a clinical trial, 30 patients with a certain blood disease are randomly assigned to two groups. One group is then randomly assigned to take the currently marketed medicine, and the other group receives the experimental medicine. Every week, the patients report to the clinic where blood tests are conducted. The clinic technician is unaware of the kind of medicine each patient is taking, and the patient is also unaware of which medicine they have been given. Which of the following is the best description of this design?

A local investment club that meets monthly has 200 members ranging in age from 27 to 81 years. A cumulative relative frequency graph of age is shown. Approximately how many members of the club are older than 60 years old?

Do children's fear levels change over time and, if so, in what ways? Several years ago, two researchers surveyed a randomly selected group of 94 third- and fourth-grade children, asking them to rate their level of fearfulness about a variety of situations. Two years later, the children again completed the same survey. The researchers computed the overall fear rating for each child in both years and want to see if there is convincing statistical evidence of a positive relationship between the scores from the two years. Here is a scatterplot of the data, along with a residual plot created from a linear regression model.

Which of the following statements is supported by these plots?

A large toy company introduces many new toys to its product line each year. The company wants to predict the demand as measured by y, first-year sales (in millions of dollars) using x, awareness of the product(as measured by the percentge of customers that have heard of the product by the end of the second month after its introduction). A random sample of 65 new products was taken, and the correlation of 0.96 between the values of x and y for these products was computed.

Which of the following statements must be true?

Suppose the null and alternate hypotheses for a significance test are defined as:

$$H_0:\ \mu=40$$

$$H_A:\ \mu<40$$

Which of the following values of $$\mu$$ will result in the highest power for this test?

A Harris poll found that 54% of U.S. adults are concerned about the economy. The poll's margin of error for 95% confidence is 3%. Which of the following statements is true?

Western lowland gorillas, whose main habitat is in central Africa, have a mean weight of 275 pounds with a standard deviation of 40 pounds. Capuchin monkeys, whose main habitat is Brazil and other parts of Latin America, have a mean weight of 6 pounds with a standard deviation of 1.1 pounds. Both distributions of weight are approximately Normal. If a particular western lowland gorilla is known to weigh 345 pounds, approximately how much would a capuchin monkey have to weigh, in pounds, to have the same standardized weight as the gorilla?

Which of the following statements about the t distribution with k degrees of freedom is (are) true?

1. 1) It is symmetric.

2. 2) It has more variability than the t distribution with k + 1 degrees of freedom.

3. 3) It is centered at 0.

Each year, a news organization polls a random sample of adult residents in a particular state to ask about the governor's job performance. In one year, 529 of the 1002 randomly selected adult residents approved of the governors's job performance. The next year, 498 of the 1009 randomly selected adult residents approved of the governor's job performance.

Do these data provide convincing evidence of a change in the proportion of all adult residents in the state who approved of the governor's job performance during these two years? Complete an appropriate significance test using $$\alpha=0.05$$