AP STATS - REVIEW FOR AP 1 TEST

In an experiment to measure the effect of fluoride "varnish" on the incidence of tooth cavities, 34 10-year-old-girls whose parents volunteered them for the study were randomly assigned to two groups. One group was given fluoride varnish annually for 4 years along with a standard dental hygiene regimen; the other group only followed the standard dental hygiene regimen. The mean number of cavities in the two groups was compared at the end of the treatments. Which of the following is a problem with this experiment? a. There was insufficient attention to the placebo effect. b. There was no control group. c. The experimental subjects should not have been limited to girls. d. The absence of replication increases the impact of random variation. e. Because the subjects were not randomly selected for the study, we cannot conclude that a reduction in cavities can be attributed to the fluoride treatment.

There was insufficient attention to the placebo effect.

A sportswriter wants to know how strongly Lafayette residents support the local minor league baseball team, the Lafayette Leopards. She stands outside the stadium before a game and interviews the first 20 people who enter the stadium. The newspaper asks you to comment on their survey method. You say, a. This is a simple random sample. The results are not biased, but the sample is too small to have high precision. b. This is a convenience sample. It will almost certainly underestimate the level of support among all Lafayette residents. c. This is a simple random sample. It gives very accurate results. d. This is a census, because all fans had a chance to be asked. It gives very accurate results. e. This is a convenience sample. It will almost certainly overestimate the level of support among all Lafayette residents.

This is a convenience sample. It will almost certainly overestimate the level of support among all Lafayette residents.

Suppose that scores on a certain IQ test are Normally distributed with mean 110 and standard deviation 15. Then about 40% of the scores are between what two numbers? a. the 25th and 75th percentiles b. 106 and 110 c. 102 and 118 d. 65 and 155 e. 80 and 140

102 and 118

There are 10 students in Mrs. Sollom's afternoon Statistics class. The maximum point total for the most recent quarter was 200 points. The point totals for the 10 students are given in the stemplot below.Key: 17 | 9 represents a point total for the quarter of 179 pointsWhat is the median point total for this class? a. 130 b. 137 c. 134.4 d. 133 e. 130.5

130.5

Here are the exam scores for the 14 students in Mrs. Gopaul's statistics class:60 61 61 65 72 75 75 78 81 81 85 89 91 98.What is the percentile of the person whose score was 65? a. 65% b. 29% c. 15% d. 85% e. 21%

21%

The density curve below shows the distribution of a variable that takes values from 0 to 1. What percent of the observations lie between 0 and 0.5? a. 80% b. 50% c. 75% d. 25% e. 20%

25%

If the heights of 99.7% of American men are between 5' 0" and 7' 0", what is your estimate of the standard deviation of the height of American men? a. 1" b. 3" c. 4" d. 12" e. 6"

4"

Forty pound bags of bird seed do not have exactly 40 pounds of seed, but the weight of seeds is approximately Normally distributed with a mean of 40 pounds and a standard deviation of 0.25 pounds. Which of the following is the best estimate of the 90th percentile for the weight of these bags of seed? a. 43.2 pounds b. 41.0 pounds c. 40.4 pounds d. 40.3 pounds e. 40.5 pounds

40.3 pounds

Below is a histogram of the heights of gold-medal-winning high jumps in the Olympic Games since 1896.Based on this histogram, what is the percentage of the winning jumps that were at least 80 inches? a. 45% b. 55% c. 10% d. 35% e. 90%

55%

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 a. 65.5 inches to 70.5 inches. b. 63 inches to 73 inches. c. 60.5 inches to 75.5 inches. d. 58 inches to 78 inches. e. None of the above.

63 inches to 73 inches.

For this density curve, what percent of the observations lie between x = 0.2 and x = 3.8? a. 72% b. 10% c. 20% d. 68% e. 28%

72%

The population of the United States is aging, though less rapidly than in other developed countries. Below is a stemplot of the percentages of residents aged 65 and older in each of the 50 states, according to the 2010 census. There are three outliers: Alaska has the lowest percentage of older residents, Utah had the second lowest, and Florida has the highest. Key: 7 | 7 represents a state with 7.7% of its residents aged 65 and olderWhat is the percentage for Utah? a. 14% b. 9% c. 90% d. 15% e. 7.7%

9

The five-number summary for the weights (in grams) of 1200 tomatoes grown in a certain greenhouse is 90, 113.5, 140, 161, and 236. How many tomatoes weighed less than 161 grams? a. 300 b. 140 c. 900 d. 236 e. 600

900

A psychologist studying the effects of "positive thinking" on cognitive ability designs the following study: 120 male volunteers are divided into two groups by random assignment. Eighty female volunteers are randomly divided into two groups of 40 by the same method. One group of 60 males and 40 females is asked to write down three things they feel that they are good at doing. The other group of 60 males and 40 females is asked to write down what they ate for breakfast. All 100 subjects then take a SAT Math practice test, and the means for the two groups are compared. Which of the following is a correct description of this study? a. A stratified random experiment b. An observational study c. A completely randomized experiment d. A randomized block experiment e. A matched pairs experiment

A randomized block experiment

A simple random sample of size n is defined to be a. a sample chosen in such a way that every unit in the population has the same chance of being selected. b. a sample chosen in such a way that each selection is made independent of every other selection. c. a sample chosen in such a way that every set of n units in the population has an equal chance to be the sample that is actually selected. d. a sample chosen in such a way that every unit in the population has a known nonzero chance of being selected. e. a sample that came from any sampling method other than convenience and voluntary response.

a sample chosen in such a way that every set of n units in the population has an equal chance to be the sample that is actually selected.

A television station is interested in predicting whether voters in its viewing area are in favor of offshore drilling. It asks its viewers to phone in and indicate whether they support/are in favor of or are opposed to this practice. Of the 2241 viewers who phoned in, 1574 (70%) were opposed to offshore drilling. The viewers who phoned can best be described as a. a voluntary response sample. b. a convenience sample. c. a probability sample. d. a simple random sample. e. a population.

a voluntary response sample.

Which of the following statements concerning residuals is true? a. The sum of the residuals is always 0. b. A plot of the residuals is useful for assessing the fit of the least-squares regression line. c. The value of a residual is the observed value of the response minus the value of the response that one would predict from the least-squares regression line. d. An influential point on a scatterplot is not necessarily the point with the largest residual. e. All of the above are true.

all of the above are true

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 interquartile range of the salaries for the employees will a. be multiplied by $3,000. b. be unchanged. c. increase by $3,000. d. increase by square root of 3000 e. decrease by $3,000.

be unchanged

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. 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 a. the placebo effect. b. an observational study. c. stratification. d. bias. e. confounding.

confounding

A survey typically records many variables of interest to the researchers involved. Below are some of the variables from a survey conducted by the U.S. Postal Service. Which of the variables is categorical? a. county of residence b. total household income, before taxes, in 1993 c. number of rooms in the dwelling d. number of people, both adults and children, living in the household e. age of respondent

county of residence

The most important advantage of experiments over observational studies is that a. observational studies cannot use random samples. b. experiments can give better evidence of causation. c. an observational study cannot have a response variable. d. confounding cannot happen in experiments. e. experiments are usually easier to carry out.

experiments can give better evidence of causation.

Consider the following scatter plot of two variables, x and y.We may conclude that the correlation between x and y a. greater than 1, because the relationship is nonlinear. b. must be close to 0, because the relationship is between x and y is clearly non-linear. c. may be exactly 1, because all the points lie of the same curve. d. must be close to -1, because the relationship is between x and y is clearly non-linear. e. is close to 1, even though the relationship is not linear.

is close to 1, even though the relationship is not linear.

Two variables are said to be negatively associated if a. larger values of one variable are associated with smaller values of the other. b. smaller values of one variable are associated with both larger or smaller values of the other. c. there is no pattern in the relationship between the two variables. d. smaller values of one variable are associated with smaller values of the other. e. larger values of one variable are associated with larger values of the other.

larger values of one variable are associated with smaller values of the other.

X and Y are two categorical variables. The best way to determine if there is a relation between them is to a. construct parallel boxplots of the X and Y values. b. compare means and standard deviations of the X and Y values. c. draw dotplots of the X and Y values. d. compare medians and interquartile ranges of the X and Y values. e. make a two-way table of the X and Y values.

make a two-way table of the X and Y values.

You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked her attitude toward the product. You think there may be large differences between women who are employed outside the home and those who are not. Because of these differences, you should use a a. completely randomized design. b. multistage sample. c. categorical variable. d. stratified design. e. randomized block design.

randomized block design.

A percentile is a measure of a. skew. b. spread. c. relative location. d. relative frequency. e. center.

relative location.

The fraction of the variability in the values of a response y that is explained by the least-squares regression with x = the explanatory variable is the a. sum of the squared residuals. b. correlation coefficient. c. slope of the least-squares regression line. d. intercept of the least-squares regression line. e. square of the correlation coefficient.

square of the correlation coefficient.

Which of the following dotplots would best be approximated by a Normal distribution?

the dot plot that has all the dots in the middle

In comparative trials in medicine, the placebo effect and subconscious bias on the part of the physicians evaluating treatment outcomes can be avoided by using a. the double-blind technique. b. randomized complete block designs. c. response variables. d. stratified random samples. e. all of the above.

the double-blind technique.

You can roughly locate the mean of a density curve by eye because it is a. the point at which the curve would balance if made of solid material. b. the point at which the curve reaches its peak. c. the point where the curvature changes direction. d. the point that divides the area under the curve into two equal parts. e. the point at which the height of the graph is equal to 1.

the point at which the curve would balance if made of solid material.

The correlation coefficient measures a. whether there is a relationship between two variables. b. whether or not a scatterplot shows an interesting pattern. c. the strength of the linear relationship between two quantitative variables. d. whether a cause and effect relation exists between two variables. e. the strength of the relationship between two quantitative variables.

the strength of the linear relationship between two quantitative variables.

Mrs. Austin measures the age, marital status and earned income of an SRS of 1463 women. The number and type of variables you have measured is a. four; one categorical and three quantitative. b. three; two categorical and one quantitative. c. three; one categorical and two quantitative. d. four; two categorical and two quantitative. e. four; one categorical and two quantitative, and one individual.

three; one categorical and two quantitative.

The computer output shown below gives the least-squares regression line for calories and protein (in grams) in one cup of 11 varieties of dried beans.Which of the following statements is a correct interpretation of the slope of the regression line? a. For each 1-gram increase in the protein content, the predicted calorie content increases by 0.024 grams. b. For each 1-unit increase in the calorie content, the predicted protein content increases by 0.063 grams. c. For each 1-gram increase in the protein content, the predicted calorie content increases by 0.063 grams. d. For each 1-gram increase in the protein content, the predicted calorie content increases by 2.08 grams. e. For each 1-unit increase in the calorie content, the predicted protein content increases by 2.08 grams.

For each 1-unit increase in the calorie content, the predicted protein content increases by 0.063 grams.

The risk of an investment is measured by the variability of the changes in its value over a fixed period, such as a year. More variation from year to year means more risk. The government's Securities and Exchange Commission wants to require mutual funds to tell investors how risky they are. A New York Times article says that some people think that "the proposed risk descriptions, especially one that goes by the daunting name standard deviation" are hard to understand. Explain to a friend what the standard deviation means, using the fact that the changes in a mutual fund's value over many years have a roughly Normal distribution. a. Start with the average (mean) change in the fund's value over many years; the actual change will be within one standard deviation of that average in about 95% of all years. b. The standard deviation is the largest change we ever expect to see in a year. c. Start with the average (mean) change in the fund's value over many years; the actual change will be within one standard deviation of that average in about 68% of all years. d. The yearly change in the fund's value will be greater than the standard deviation half the time and less than the standard deviation half the time. e. The standard deviation is the distance between the lower and upper quartiles, so it spans half the yearly changes in the fund's value.

Start with the average (mean) change in the fund's value over many years; the actual change will be within one standard deviation of that average in about 68% of all years.

The bar graph at right shows the distribution of religious affiliation around the world. Which of the following statement best describes what is wrong with this graph? a. The "other" category should be subdivided into all the religions included. b. Since this is a bar graph, the bars should be touching each other. c. The bars should be in decreasing order of size. d. The vertical scale should be in numbers of people, not percentages. e. Starting the vertical scale at 5 distorts the relative frequency of the religions.

Starting the vertical scale at 5 distorts the relative frequency of the religions.

The scatterplot below shows the relationship between carbohydrates and protein in one-cup servings of 15 different varieties of beans. The unusual point in the upper left part of the plot is for navy beans, with 15.8 grams of protein and 15.8 grams of carbohydrates. Which of the following best describes how correlation would change if we removed navy beans from the data set? a. The correlation would be closer to 1, because the remaining data would have a stronger positive relationship. b. The correlation would be closer to 0, because the standard deviation of the residuals would be smaller. c. Correlation could no longer be calculated, because the remaining data would fall into two distinct groups. d. The correlation would be closer to 1, because there would be fewer individuals in the data set. e. The correlation would be closer to 0, because the data would more closely resemble a straight line.

The correlation would be closer to 1, because the remaining data would have a stronger positive relationship.

A least-squares regression line for predicting weights of basketball players based upon their heights produced the residual plot below. What does the residual plot tell you about the linear model? a. There are not enough data points to draw any conclusions from the residual plot. b. The curved pattern in the residual plot suggests that there is no association between the weight and height of basketball players. c. A residual plot is not an appropriate means for evaluating a linear model. d. The curved pattern in the residual plot suggests that the linear model is not appropriate. e. The linear model is appropriate, because there are approximately the same number of points above and below the horizontal line in the residual plot.

The curved pattern in the residual plot suggests that the linear model is not appropriate.

The graph below is a Normal probability plot for the amount of rainfall (in acre-feet) obtained from 26 randomly selected clouds that were seeded with silver oxide. Which of the following statements about the shape of the rainfall distribution is true? a. The distribution is Normal. b. The distribution has no potential outliers. c. The distribution is skewed to the left. d. The distribution is skewed to the right e. The distribution is approximately Normal

The distribution is skewed to the right

One hundred people work at Lagtime Internet Services. Suppose after a particularly successful year, the president of the company decided to double his own salary and not change anyone else's. Assuming the president makes more than anyone else, which of the following statements about changes in measures of center and spread is true? a. The mean will increase, but the median, standard deviation, and interquartile range will stay the same. b. The mean and interquartile range will increase, but the median and standard deviation will stay the same. c. The mean, standard deviation, and interquartile range will increase, but the median will stay the same. d. The mean, median, standard deviation, and interquartile range will all increase. e. The mean and standard deviation will increase, but the median and interquartile range will stay the same.

The mean and standard deviation will increase, but the median and interquartile range will stay the same.

There are 10 students in Mrs. Thomas's afternoon Statistics class. The maximum point total for the most recent quarter was 200 points. The point totals for the 10 students are given in the stemplot below.Key: 17 | 9 represents a point total for the quarter of 179 pointsThe mean score is 134.4 points and the standard deviation is 18.64 points. If the score of 179 was supposed to be 129 how would the value of the mean and standard deviation change? a. The mean would increase and the standard deviation would decrease. b. The mean would decrease and the standard deviation would increase. c. The mean would remain about the same and the standard deviation would remain about the same. d. The mean would increase and the standard deviation would increase. e. The mean would decrease and the standard deviation would decrease.

The mean would decrease and the standard deviation would decrease.