AP Optional Final Semester 1 - Review

A farmer wishes to determine which of two brands of baby pig pellets, Kent or Moormans, produces better weight gains. Two of his sows each give birth to litters of 10 pigs on the same day, so he decides to give the baby pigs in litter A only Kent pellets, while the pigs in litter B will get only Moormans pellets. After four weeks, the average weight gain for pigs in litter A is greater than the average weight gain for pigs in litter B. The brand of pellets is

the explanatory variable

Jessica was studying starfish populations and collected starfish of the species Pisaster. She was interested in the distribution of sizes of starfish on a certain shoreline. One measure of size is "arm length." Below is a cumulative relative frequency distribution for the arm length, in centimeters, of 102 Pisaster individuals

yes, this star fish is approximately at the 90th percentile for Pisaster arm length

A consumer group surveyed the prices for a certain item in five different stores, and reported the average price as $15. We visited four of the five stores, and found the prices to be $10, $15, $15, and $25. Assuming that the consumer group is correct, what is the price of the item at the store that we did not visit?

$10

The mean score on Mrs. Henchan's AP statistics test was 68.5 and the standard deviation was 15.4. The scores were distinctly skewed to the left. Daphne's test score was 58. Which of the following is closest to Daphne's z-score?

-0.68

A researcher wishes to study how the average weight y (in kilograms) of children changes during the first year of life. He plots these averages versus the age x (in months) and decides to fit a least-squares regression line to he data with x as the explanatory variable and y as the response variable. He computes the following quantities... What is the slope of the least-squares regression line?

0.30

The area under the standard Normal curve corresponding to -0.5 < z < 1.2 is closest to what value?

0.5764

The cumulative relative frequency graph below shows the distribution of lengths (in centimeters) of fingerlings at a fish hatchery. The interquartile range for this distribution is approximately

1.2 centimeters

In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y = 10 + 0.9x where y is the final-exam score and x is the score on the first test. Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual?

2

You measure the age (in years), weight (in pounds), and marital status (single, married, divorced, or widowed) of 1400 women. How many variables did you measure?

3

Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. What percent of bags that will contain between 16.0 and 16.1 ounces?

34

The five-number summary of test scores for the 600 students in Mrs. Hughes's Statistics class School is 52, 65, 78, 85, and 96. How many students scored higher than 65?

450

The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. Only about 5% of young men have heights outside the range

63 to 73 inches

A fisheries biologist studying whitefish in a Canadian lake collected data on the length (in centimeters) and egg production for 25 female fish. A scatter plot of her results and computer regression analysis of egg production versus fish length are given below. Note that the Number of eggs is given in thousands (i.e., "40" means 40,000 eggs). Which of the following statements can be made based upon the computer output?

69.7% of the variability in egg production can be accounted for by the linear regression with x = fish length.

Here are the exam scores for the 15 students in Mr. Kirk's statistics class: 72 75 75 78 81 81 85 89 90 90 90 91 95 95 98. Karen was at the 20th percentile of the distribution. What score did Karen earn on the exam?

75

The pie chart at right describes the distribution of favorite school subjects for 300 high school students. How many students reported that "Math" is their favorite subject?

78

A statistics teacher asks the 29 students in his statistics class how many minutes they spent on one assignment. The distribution of the variable "time on homework" is

A description of what values the variable takes and how often it takes them

A television station is interested in predicting whether voters in its listening area are in favor of federal funding for railroad improvements. It asks its viewers to phone in and indicate whether they are in favor or opposed to this. Of the 2241 viewers who phoned in, 1574 (70%) were opposed to offshore drilling. The viewers who phoned can be best described as

A voluntary response sample

Which of the following is not a major principle of good design for all experiments?

Blocking

A fisheries biologist studying whitefish in a Canadian lake collected data on the length (in centimeters) and egg production for 25 female fish. A scatter plot of her results and computer regression analysis of egg production versus fish length are given below. Note that the Number of eggs is given in thousands (i.e., "40" means 40,000 eggs). What is the equation of the least-squares regression line?

Eggs = -142.74 + 39.25 (Length)

The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. Which of the following statements are supported by the scatterplot?

I. There is a positive association between height and volume II. There is an outlier in the plot. III. As the height of a cerry increased, the volume of useable lumber it yields increased.

For the histogram below, what are the correct locations of the mean and median? Note that the graph is numerically precise- only the relative positions are important.

II is the mean and III is the median.

A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is y = 1344 - 19x. When the temperature goes up 1 degree, what happens to the gas usage predicted by the regression line?

It goes down 19 cubic feet.

Below is a scatter plot (with the least squares regression line) for calories and protein (in grams) in one cup of 11 varieties. The computer output for this regression is below the plot. One cup of dried soybeans contains 846 calories. Which statement is correct?

It would be inappropriate to predict the protein content of soybeans with this regression model, because their calorie content is well beyond the range of these data.

The Normal curve below describes the death rates from heart disease per 100,00 people in developed countries The mean and standard deviation of this distribution have approximately what values?

Mean = 200; standard deviation = 67

The histogram below shows the distribution of heights for 100 randomly selected school children in Britain. Which of the following descriptions best fits this distribution?

Roughly symmetric, centered at about 150, range: 80

A public opinion poll in Ohio wants to determine whether registered voters in the state approve of a measure to ban smoking in all public areas. The researchers select a simple random sample of 50 registered voters from each county in the state and ask whether they approve or disapprove of the measure. This is an example of a

Stratified random sample

The mean height of men in the United States if 69 inches and the standard deviation is 3 inches. For U.S. women, the mean is 64 inches and the standard deviation is 2.7 inches. The tallest women in the Women's national Basketball Association is Brittney Griner, who is 80 inches tall (6 feet 8 inches). The tallest current player in the Men's NBA is Hasheem Thabeet, who is 87 inches tall (7 feet 5 inches). Which player is taller relative to others of the same sex in the U.S?

Thabeet, because his z-score is greater

The five-number summary of the distribution of scores on the final exam in Psych 001 last semester was 18, 39, 62, 76, and 100. Which of the following best describes the location of the 80th percentile?

The 80th percentile is between 76 and 100

All but one of the following statements contains an error. Which statement could be correct?

The correlation between mid-August soil moisture ad the per-acre yield of tomatoes is r = 0.53

You have data for many families on the parents' income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school for longer. When you make a scatterplot,

The explanatory variable is parents' income, and you expect to see a positive association

The time it takes people to finish a certain kind of puzzle is strongly skewed to the right. Which of the following statements is true about the mean and median of this distribution?

The mean will be greater than the median.

Shown below are box plots describing the distribution of prices paid for homes in two suburbs of Columbus, Ohio over a single 30-day period in 2016. Which of the following statements is supported by the information in this graph?

The median house price in Dublin is higher than 75th percentile of house price in Westerville.

Which one of the following potential problems is addressed by performing a blind study?

The placebo effect

Can you predict a person's shoe size from their height? The computer output below provides information on a regression analysis of these variables for 12 randomly selected high school students in England. Both height and foot length are measured in centimeters Which of the following is a correct interpretation of S = 1.223?

The typical error in predicting foot length from height based on this regression model is about 1.22 cm.

In a study of the link between high blood pressure and cardiovascular disease, a group of white people aged 35 to 64 was followed for 5 years. At the beginning of the study, each man had his blood pressure and it was classified as either "low" systolic blood pressure (less than 140 mm Hg) or "high" blood pressure (140 mm Hg or higher). The following table gives the number of men in each blood pressure the number of deaths from cardiovascular during the 5-year period.

These data are consistent with the idea that there is a link between high blood pressure and death from cardiovascular disease.

Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side effect of drowsiness. To investigate this question, the researchers randomly assigned 100 adult volunteers who suffer from allergies to two groups. They gave the new medication to the subjects in one group and an existing medication to the subjects in the other group. Forty-four percent of those in the treatment group and 28$ of those in the control group reported a significant reduction in their allergy symptoms without any drowsiness. Which of the following best describes the interference the researchers can make based in his results?

They can make inferences about cause and effect , but not about the populations form which the samples were taken.

Eighty volunteers who currently use a certain brand of over-the-counter allergy medication have been recruited to participate in a trial of a new allergy medication. The volunteers are randomly assigned to one of two groups. One group continues to take their current medication, the other group switches to the new experimental medication. Each is asked after two weeks if their allergy symptoms are worse, better, or about the same as they were at the start of the study. Which of the follow best describes a conclusion that can be drawn from this study?

We can determine whether the new drug reduces symptoms more than the old drug for the subjects in the study.

A study sponsored by American Express Co. and the French government tourist office found that old stereotypes about French unfriendliness were not true. The respondents were more than 1000 Americans who have visited France more than once for pleasure over the past two years. The results of this study are probably

biased, overstating the extent to which the old stereotypes were not true

Does caffeine improve exam performance? Suppose all students in the 8:30 section of a course are given a "treatment" (two cups of coffee) and all students in the 9:30 section are not permitted to have any caffeine before a mid-term exam. (Answer questions 11 and 12) 11. Unfortunately, any systematic difference between the two sections on the exam might be due to the fact that the 8:30 and 9:30 classes have different instructors. This is an example of

confounding

An experiment was conducted by some students to explore the nature of the relationship between a person's heart rate (measured in beats per minute) and the frequency at which that person stepped up and down on steps of various heights. Three rates of stepping and two different step heights were used. A subject performed the activity (stepping at one of the three stepping rates at one of the two possible heights) for three minutes. Heart rate was then measured at the end of this period. The variables "stepping rate" and "step height" are the

factors

We wish to draw a sample of 5 without replacement from a population of 50 households. Suppose the households are number 01, 02,...50, and suppose that the relevant line of the random number table 11362 35692 90842 46843 The households selected are

households 11, 36, 23, 08, and 42.

A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year... Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000). The mean salary for the employees will

increase by $3,000

The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. If the data point (65, 70) were removed from this study, how would the value of the correlation r change?

r would be larger, because this point does not fall in the pattern for the rest of the data.