AP STATS
Tests and Samples
Multiple Choice
Terms
Identifying True Statements
100
Which of the following are true about sampling? 1. Sampling error is the natural variation that is normally present as a result of the sample. 2. Sampling error can be eliminated by taking a larger sample. 3. An attempted census will result in unbiased results. 4. Sampling bias can be eliminated by using a sampling method that incorporates proper randomization.
What is 1. Sampling error is the natural variation that is normally present as a result of the sample. AND 4. Sampling bias can be eliminated by using a sampling method that incorporates proper randomization.
100
The city has five property classifications, single family homes, apartments, condominiums, temporary housing(hotel and campgrounds), and retail property. Randomly select ten residents from each category.
What is Stratified.
100
A researcher wants to compare performance of three types of pain relievers in volunteers suffering from arthritis. Because people of different age may act differently to medication, the subjects are split into two groups; under 60 and over 60. Subjects in each group are randomly assigned to take one of the medications. Twenty minutes later they rate their levels of pain. This experiment... A. Is completely randomized B. Uses matched pairs C. Has one factor (medication) blocked by age D. Has one factor (age) blocked by a type of medication E. Has two factors, age and medication
What is C. Has one factor (medication) blocked by age
100
A study that looks at the past data of all citizens of a town and tries to make connections to an association is called....
What is a retrospective study.
100
Which of the following statements is true? I. The center of a confidence interval is a population parameter. II. The bigger the margin of error, the smaller the confidence interval. III. The confidence interval is a type of point estimate. IV. A population mean is an example of a point estimate. A. I only B. II only C. III only D. IV only E. None of the above
What is E. none of the above. The center of a confidence interval is a sample statistic, not a population parameter. The confidence interval is equal to the sample statistic plus or minus the margin of error; so the confidence interval gets bigger as the margin of error gets bigger.
200
Five white and five black marbles are in a box. Without looking, three marbles are taken from the box without replacement. What is the probability that all three are black? A. 25/144 B. 1/12 C. 1/8 D. 3/50 E. 1/10
What is B.1/12
200
Each property owner has a 5-digit ID number. Use a random number table to choose forty numbers.
What is a Simple Random Sample
200
An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers of each brand. Is this an example of a SRS? A. Yes because each buyer in the sample was randomly sampled. B. Yes, because each buyer in the sample had an equal chance of being sampled. C. Yes, because car buyers of each brand were equally represented in the sample. D. No, because every possible 400 buyer sample did not have an equal chance of being chosen. E. No, because the population consisted of purchasers of four different brands of cars.
What is D. No, because every possible 400 buyer sample did not have an equal chance of being chosen.
200
The probability of a type one error...
What is Alpha or level of significance
200
Which of the following statements is true. I. The standard error is computed solely from sample attributes. II. The standard deviation is computed solely from sample attributes. III. The standard error is a measure of central tendency. A. I only B. II only C. III only D. I and II E. I and III
What is A. I only. The standard error can be computed from a knowledge of sample attributes- sample size and sample statistics. The standard deviation cannot be computed solely from sample attributes; it requires a knowledge of one or more population parameters. The standard error is a measure of variability, not a measure of central tendency.
300
Suppose the probability of encountering an American who practices a particular religion is 0.014. What are the mean and standard deviation for the number of Americans in a random sample of 500 who practice this religion. A. mean 0.014; standard deviation 0.0006 B. mean 0.014; standard deviation 0.0053 C. mean 7; standard deviation 0.0006 D. mean 7; standard deviation 0.0053 E. mean 7; standard deviation 2.627
What is E. mean 7; standard deviation 2.627
300
At the start of each week, survey every tenth person who arrives at the city park.
What is systematic and convenience.
300
A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test? A. 82 B. 88 C. 100 D. 112 E. 118
What is E.118
300
The probability of a type two error.
What is Beta.
300
Which of the following statements is true? I. A sample survey is an example of an observational study. II. An observational study requires fewer resources than an experiment. III. The best method for investigating casual relationships is an observational study. A. I only B. II only C. III only D. All of the above E. None of the above
What is A. In a sample survey, the researcher does not assign treatments to survey respondents. Therefore, a sample survey is not an experimental study; rather it is an observational study. An observational study may or may not require fewer resources (time, money, and manpower) than an experiment. The best method for investigating casual relationships is an experiment- not an observational study- because an experiment features randomized assignment of subjects to treatment groups. Randomization "evens out" the effects of extraneous variables, which makes it easier for the researcher to identify casual effect of treatment variables.
400
A distribution is about N (25,5). According to the Empirical Rule, approximately what percent of the data would you expect to lie between 20 and 25? A. 30% B. 34% C. 60% D. 68% E. 95%
What is B. 34%
400
Acme Toy Company sells baseball cards in packages of 100. Three types of players are represented in each package -- rookies, veterans, and All-Stars. The company claims that 30% of the cards are rookies, 60% are veterans, and 10% are All-Stars. Cards from each group are randomly assigned to packages. Suppose you bought a package of cards and counted the players from each group. What method would you use to test Acme's claim that 30% of the production run are rookies; 60%, veterans; and 10%, All-Stars (A) Chi-square goodness of fit test (B) Chi-square test for homogeneity (C) Chi-square test for independence (D) One-sample t test (E) Matched pairs t-test
What is (A). The chi-square goodness of fit test is used to find out whether an observed pattern of categorical data is consistent with a specified distribution. In this problem, we are dealing with a categorical variable -- the type of baseball card. And we want to determine whether the distribution in our package is consistent with the production distribution claimed by Acme Toy Company. So the chi-square goodness of fit test is appropriate.
400
Suppose we want to estimate the average weight of an adult male in DeKalb County, Georgia. We draw a random sample of 1,000 men from a population of 1,000,000 men and weigh them. We find that the average man in our sample weighs 180 pounds, and the standard deviation of the sample is 30 pounds. What is the 95% confidence interval? A. 180 +/- 1.86 B. 180 +/- 3.0 C. 180 +/- 5.88 D. 180 +/- 30 E. None of the above
What is A.
400
This consists of two variables, an explanatory and a response variable, usually quantitative.
What is bivariate data.
400
In hypothesis testing, which of the following statements is always true? I. The P-value is greater than the significance level. II. The P-value is computed from the significance level. III. The P-value is the parameter in the null hypothesis. IV. The P-value is a test statistic. V. The P-value is a probability. (A) I only (B) II only (C) III only (D) IV only (E) V only
What is (E). The P-value is the probability of observing a sample statistic as extreme as the test statistic. It can be greater than the significance level, but it can also be smaller than the significance level. It is not computed from the significance level, it is not the parameter in the null hypothesis, and it is not a test statistic
500
With a level of 5%, what is the power of a test against an alternative for which the probability of a Type II error is 3%? A. 3% B. 5% C. 95% D. 97% E. the power cannot be determined from the information given
What is D. 97%
500
In the context of regression analysis, which of the following statements are true? I. When the sum of the residuals is greater than zero, the model is nonlinear. II. A random pattern in the residual plot indicates that linear regression is appropriate. III. Influential points always reduce the correlation coefficient. (A) I only (B) II only (C) III only (D) I and II (E) I, II, and III
What is (B). Researchers use residual plots to decide whether data fit a linear or a non-linear model. A random pattern of residuals suggests that a linear model is appropriate; a non-random pattern suggests that a non-linear model may be appropriate. The sum of the residuals is always zero, whether the regression model is linear or nonlinear. And influential points often increase the correlation coefficient.
500
Suppose X and Y are independent random variables. The variance of X is equal to 16; and the variance of Y is equal to 9. Let Z = X - Y. What is the standard deviation of Z? (A) 2.65 (B) 5.00 (C) 7.00 (D) 25.0 (E) It is not possible to answer this question, based on the information given
What is B. The solution requires us to recognize that Variable Z is a combination of two independent random variables. As such, the variance of Z is equal to the variance of X plus the variance of Y. Var(Z) = Var(X - Y) = Var(X) + Var(Y) = 16 + 9 = 25 The standard deviation of Z is equal to the square root of the variance. Therefore, the standard deviation is equal to the square root of 25, which is 5.
500
Using a model to predict values far outside the range of the explanatory variable, which is prone to creating unreasonable predictions.
What is extrapolation.
500
A national consumer magazine reported the following correlations. ◾The correlation between car weight and car reliability is -0.30. ◾The correlation between car weight and annual maintenance cost is 0.20. Which of the following statements are true? I. Heavier cars tend to be less reliable. II. Heavier cars tend to cost more to maintain. III. Car weight is related more strongly to reliability than to maintenance cost. (A) I only (B) II only (C) III only (D) I and II (E) I, II, and III
What is E. The correlation between car weight and reliability is negative. This means that reliability tends to decrease as car weight increases. The correlation between car weight and maintenance cost is positive. This means that maintenance costs tend to increase as car weight increases. The strength of a relationship between two variables is indicated by the absolute value of the correlation coefficient. The correlation between car weight and reliability has an absolute value of 0.30. The correlation between car weight and maintenance cost has an absolute value of 0.20. Therefore, the relationship between car weight and reliability is stronger than the relationship between car weight and maintenance cost.
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