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?

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Answer explanation

When looking for the probability of a first success use the Geometric Probability Distribution.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.8

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 double-blind, completely randomized experiment, with the currently marketed medicine and the experimental medicine as the treatment groups.

• A single-blind, completely randomized experiment, with the currently marketed medicine and the experimental medicine as the treatment groups.

• A double-blind, matched-pairs design, with the currently marketed medicine and the experimental medicine forming a pair.

• A double-blind, completely randomized block experiment that is not a matched pairs design, with the currently marketed medicine and the experimental medicine as two blocks.

• A double-blind, randomized observational study.

Tags

CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.5

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?

• 20

• 40

• 78

• 90

• 110

Answer explanation

Find your x-value and look at the corresponding y-value to determine your answer.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.A.1

CCSS.HSS.ID.B.5

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?

• The abundance of outliers and influential observations in the plots means that the conditions for inference are clearly violated.

• The plots contain strong evidence that the standard deviation of the response variable about the population regression line is not approximately the same for each x-value.

• These plots call into question the validity of the condition that the response variable varies normally about the least-squares regression line for each x-value.

• The linear model isn't appropriate here because the residual plot shows no association.

• The is no clear evidence that the conditions for inference are violated.

Answer explanation

Look up the conditions for inference for a slope.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.A.3

CCSS.HSS.ID.B.6

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?

• The probability that the least-squares regression line accurately predicts the first-year sales is 0.96.

• For each increase of 1% in awareness of the new product, the predicted sales will go up 0.96 million dollars.

• About 92% of the time, the percentage of people who have heard of the product by the end of the second month.

• About 92% of first-year sales can be accounted for by the percentage of people who have heard of the product by the end of the second month.

• About 92% of the variation in first-year sales can be accounted for by the least-squares regression line with the percentage of people who have heard of the product by the end of the second month as the explanatory variable.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8

Answer explanation

Power is the probability of rejecting the null hypothesis when you should. Considering the alternate hypothesis, which of these values should make rejecting the null more likely?

Tags

CCSS.HSS.ID.A.4

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?

• There is a 95% probability that the percentage of all U.S. adults who are concerned about the economy is between 51% and 57%.

• The poll used in this method that provides an estimate within 0.03 of the proportion of all U.S. adults who are concerned about the economy in 95% of samples.

• If Harris conducts another poll using the same method, the percentage of U.S. adults in the sample who are concerned about the economy will be between 51% and 57%.

• There is a 3% chance that the interval from 0.51 to 0.57 misses the proportion of all U.S. adults who are concerned about the economy.

• The poll used a method that would result in an interval that contains 54% in 95% of all possible samples of the same size from the same population of U.S. adults.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.IC.B.6

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?

• 4.075

• 7.750

• 7.925

• 8.200

• There is not enough information to determine the weight of a capuchin monkey.

Answer explanation

The standardized weight is the z-score.

Tags

CCSS.HSS.ID.A.4

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.

• 1 Only

• 2 Only

• 3 Only

• 1 & 3

• 1, 2, & 3

Answer explanation

As degrees of freedom increase the t distribution grows less and less variable.

Tags

CCSS.HSS.ID.A.3

Answer explanation

Perform a complete hypothesis test with variables, hypotheses, conditions, the test identified, standardized test statistic, p-value, and conclusion in context.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.4

CCSS.HSS.ID.B.5