1



1. In a statistics class with 136 students, the professor records how much money each student has

in his or her possession during the first class of the semester. The histogram below is of the

data collected.

[pic]

|The histogram |

|A) is skewed right. |

|B) has an outlier. |

|C) is asymmetric. |

|D) has a mean less than 30. |

|E) all of the above. |

|2. |A set of data has a median that is much larger than the mean. Which of the following statements is most consistent with this |

| |information? |

|A) |A stemplot of the data is assymetrical. |

|B) |A stemplot of the data is skewed left. |

|C) |A stemplot of the data is skewed right. |

|D) |The data set must be so large that it would be better to draw a histogram than a stemplot. |

|E) |A stemplot of the data is symmetric. |

| 3. In a statistics class with 136 students, the professor records how much money |

|each student has in his or her possession during the first class of the semester. The |

|histogram below is of the data collected. |

|[pic] |

|From the histogram, which of the following is true? |

|A) |The mean is much larger than the median. |

|B) |The mean is much smaller than the median. |

|C) |The mean must be at least $10 below the median. |

|D) |It is impossible to compare the mean and median for these data. |

|E) |The mean and median are approximately equal. |

|The Insurance Institute for Highway Safety publishes data on the total damage |

|suffered by compact automobiles in a series of controlled, low-speed collisions. |

|A sample of the data in dollars, with brand names removed, is |

|1000 |

|600 |

|800 |

|1000 |

| |

|The interquartile range of the data is |

| A) 300. B) 200. C) 400. D) 450. E) none of the above. |

| |

4. 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. For convenience, the data are ordered.

|28 |31 |34 |35 |37 |41 |42 |42 |42 |47 |

|49 |51 |52 |52 |60 |61 |67 |72 |75 |77 |

Find the upper and lower bounds to determine if any outliers exist in this data.

Chapter 2

| 6. If bricks are fired at a temperature above 1125°F, they will crack and must be |

|discarded. If the bricks are placed randomly throughout the kiln, the proportion of |

|bricks that crack during the firing process is closest to |

| A) 0.62%. B) 2.28%. C) 6.2%. D) 47.72%. E) 49.38%. |

| |

| |

|7. A company produces boxes of soap powder labeled “Giant Size 32 Ounces.” The |

|actual weight of soap powder in a box has a normal distribution with a mean of 33 |

|ounces and a standard deviation of 0.7 ounces. What proportion of boxes are |

|underweight (i.e., weigh less than 32 ounces)? |

| A) 0.0764. B) 0.2420. C) 0.4236. D) 0.7580. E) 0.9236. |

Chapter 3

| 8. Consider the scatterplot below. |

| |

|[pic] |

|According to the scatterplot, which of the following is a plausible value for the |

|correlation coefficient between weight and MPG? |

| A) [pic]. B) [pic]. C) [pic]. D) 0.2. E) 0.7. |

| |

9.

| |Consider the scatterplot below. |

| |[pic] |

| |The correlation between X and Y is approximately |

| |A) 0.999. B) 0.8. C) 0.5. D) 0. E) –0.7. |

10.

| In a statistics course, a linear regression equation was computed to predict a |

|student’s final exam score from his/her score on the first test. The equation of the |

|least-squares regression line was |

| |

|[pic] |

| |

|where y represents the final exam score and x is the score on the first exam. |

|Suppose Joe scores a 90 on the first exam. What would be the predicted value of |

|his score on the final exam? |

|A) |91. |

|B) |90. |

|C) |89. |

|D) |81. |

|E) |It cannot be determined from the information given. We also need to know the correlation coefficient. |

11.

|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 children’s age X (in months) and decides to fit a least-squares regression line to the data with X as |

|the explanatory variable and Y as the response variable. He computes the following quantities. |

|r = correlation between X and Y = 0.9 |

|[pic]= mean of the values of X = 6.5 |

|[pic] = mean of the values of Y = 6.6 |

|sX = standard deviation of the values of X = 3.6 |

|sY = standard deviation of the values of Y = 1.2 |

| |

|The slope of the least-squares line is |

|A) 0.30. B) 0.88. C) 1.01. D) 2.7. E) 3.0. |

The scatterplot below plots, for each of the 50 states, the percent of 18-year-olds in the state Y in 1990 that graduated from high school versus the state’s infant mortality rate (deaths per 1,000 births) X in 1990.

.

[pic] [pic]

|12. |Referring to the information above, the least-squares regression line was fitted to the data in the scatterplot and the residuals |

| |were computed. A plot of the residuals versus the 1990 population in the state is given above. |

| | |

| |This plot suggests |

|A) |that states with larger populations have lower infant mortality rates due to superior hospital facilities. |

|B) |that high infant mortality rates imply low nutrition and thus higher dropout rates later in life, but only for states with|

| |small populations. |

|C) |that population may be a lurking variable in understanding the association between infant mortality rate and percent |

| |graduating from high school. |

|D) |that high infant mortality rates imply low nutrition and thus higher dropout rates later in life, but only for states with|

| |large populations. |

|E) |none of the above. |

Chapter 5

A study of human development showed two types of movies to groups of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by children watching the different kinds of movies. One kind of movie was shown at 8 a.m. (right after the children had breakfast) and another at 11 a.m. (right before the children had lunch). It was found that during the movie shown at 11 a.m., more crackers were eaten than during the movie shown at 8 a.m.. The investigators concluded that the different types of movies had an effect on appetite.

|13. |The results cannot be trusted because |

|A) |the study was not double-blind. Neither the investigators nor the children should have been aware of which movie was being|

| |shown. |

|B) |children are usually too sleepy early in the morning to watch movies. |

|C) |the investigators should have used several bowls, with crackers randomly placed in each. |

|D) |the time the movie was shown is a confounding variable. |

|E) |the investigators were biased. They knew beforehand what they hoped the study would show. |

|14. |The response variable in this experiment is |

|A) |the number of crackers eaten. |D) |the bowls. |

|B) |the different kinds of movies. |E) |the time the movie was shown. |

|C) |the children in the study. | | |

15. A study of cell phones and the risk of brain cancer looked at a group of 469 people who have

brain cancer. The investigators matched each cancer patients with a person of the same sex, age,

and race who did not have brain cancer, then asked about use of cell phones. This is

A) An observational study

B) An uncontrolled experiment

C) A randomized comparative experiment

D) Matched pairs experiment

E) A survey

16. A researcher wished to compare the effects of two fertilizers on the yield of a soybean crop. She

has 20 plots of land available and she decides to a paired experiment – using 10 pairs of plots.

Which would be the best way to choose the pairs?

A) Use a random digit table to divide the 20 plots into 10 pairs and then, for each pair, flip a coin to assign the fertilizers to the 2 plots

B) Subjectively divide the 20 plots into 10 pairs (making the plots within a block as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots

C) Use a random digit table to divide the 20 plots into 10 pairs and then use the random digit table again to decide upon the fertilizer to be applied to each pair

D) Flip a coin to divide the 20 plots into 10 pairs and then, for each pair, use the random digit table to assign the fertilizers to each pair

E) Use a random digit table to assign the 2 fertilizers to the 20 plots and then use the random digit table again to place the plots into 10 pairs.

Chapter 6

|17. |I toss a thumbtack 60 times and it lands point up on 35 of the tosses. The approximate probability of landing point up is |

| |A) 35. B) 0.35. C) 0.58. D) 0.65. E) 58. |

|18. |Suppose we have a loaded die that gives the outcomes 1–6 according to the following probability distribution: |

| | |

| |X |

| |1 |

| |2 |

| |3 |

| |4 |

| |5 |

| |6 |

| | |

| |P(X) |

| |0.1 |

| |0.2 |

| |0.3 |

| |0.2 |

| |0.1 |

| |0.1 |

| | |

| | |

| |Note that for this die all outcomes are not equally likely, as they would be if the die were fair. If this die is rolled 6000 |

| |times, the number of times we get a 2 or a 3 should be about |

| |A) 1000. B) 2000. C) 3000. D) 4000. |

| |E) The answer cannot be determined since the probabilities are only approximate. |

|19. |I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which |

| |of the following is an appropriate sample space S for the possible outcomes? |

|A) |S = {red, black}. |

|B) |S = {(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for the event “the |

| |first card is red and the second card is red.” |

|C) |S = {0, 1, 2}. |

|D) |All of the above. |

|E) |The results will vary since the cards are drawn without replacement. |

|20. |Event A occurs with probability 0.3. If event A and B are disjoint, then |

| |A) P(B) ≤ 0.3. B) P(B) ≥ 0.3. C) P(B) ≤ 0.7. D) P(B) ≥ 0.7. |

| |E) P(B) = 0.21. |

|21. |Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive), then |

|A) |P(A and B) = 0.16. |D) |P(A or B) = 0.16. |

|B) |P(A and B) = 0.84. |E) |P(A or B) = 1. |

|C) |P(A and B) = 1. | | |

|22. |Suppose there are three cards in a deck, one marked with a 1, one marked with a 2, and one marked with a 5. You draw two cards |

| |at random and without replacement from the deck of three cards. The sample space S = {(1, 2), (1, 5), (2, 5)} consists of these |

| |three equally likely outcomes. Let X be the sum of the numbers on the two cards drawn. Which of the following is the correct set|

| |of probabilities for X? |

|A) |X |

| |1 |

| |2 |

| |5 |

| | |

| |P(X) |

| |1/3 |

| |1/3 |

| |1/3 |

| | |

|B) |X |

| |3 |

| |6 |

| |7 |

| | |

| |P(X) |

| |1/3 |

| |1/3 |

| |1/3 |

| | |

|C) |X |

| |3 |

| |6 |

| |7 |

| | |

| |P(X) |

| |3/16 |

| |6/16 |

| |7/16 |

| | |

|D) |X |

| |3 |

|E) |6 |

| |7 |

| | |

| |P(X) |

| |1/4 |

| |1/2 |

| |1/4 |

| | |

| |X |

| |1 |

| |2 |

| |5 |

| | |

| |P(X) |

| |1/4 |

| |1/2 |

| |1/4 |

| | |

Use the following to answer questions 32-33:

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1.

|23. |Referring to the information above, the conditional probability of A given B |

|A) |is 0.3. |

|B) |is 0.2. |

|C) |is 1/6. |

|D) |is 0.1. |

|E) |cannot be determined from the information given. |

|24. |Referring to the information above, we may conclude |

|A) |that events A and B are independent. |D) |that events A and B are disjoint. |

|B) |that events A and B are complements. |E) |none of the above. |

|C) |that either A or B always occurs. | | |

|25. |The probability of a randomly selected adult having a rare disease for which a diagnostic test has been developed is 0.001. The |

| |diagnostic test is not perfect. The probability the test will be positive (indicating that the person has the disease) is 0.99 |

| |for a person with the disease and 0.02 for a person without the disease. The proportion of adults for which the test would be |

| |positive is |

| |A) 0.00002. B) 0.00099. C) 0.01998. D) 0.02097. E) 0.02100. |

Chapter 7

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5, you win $1; if number of spots showing is 6, you win $4; and if the number of spots showing is 1, 2, or 3, you win nothing. Let X be the amount that you win on a single play of the game.

|26. |Referring to the information above, the expected value of X is |

| |A) $0. B) $1. C) $1.33. D) $2.50. E) $4. |

|27. |Referring to the information above, the variance of X is |

| |A) 1. B) 1.414. C) 3/2. D) 2. E) 13/6. |

|28. |Suppose X is a random variable with mean μX and standard deviation σX. Suppose Y is a random variable with mean μY and standard |

| |deviation σY. The mean of X + Y is |

|A) |μX + μY. |

|B) |(μX/σX) + (μY/σY). |

|C) |μX + μY, but only if X and Y are independent. |

|D) |(μX + μY)/(σX+σY). |

|E) |(μX/σX) + (μY/σY), but only if X and Y are independent. |

|29. |Suppose X is a random variable with mean μX and standard deviation σX. Suppose Y is a random variable with mean μY and standard |

| |deviation σY. The variance of X + Y is |

|A) |σX + σY. |

|B) |(σX)2 + (σY)2. |

|C) |σX + σY, but only if X and Y are independent. |

|D) |(σX)2 + (σY)2, but only if X and Y are independent. |

|E) |(σX + σY)2. |

|30. |Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the|

| |number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample |

| |space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)}. X, the sum of the numbers on the two balls |

| |selected, has the following probability distribution: |

| | |

| | |

| |X |

| |3 |

| |4 |

| |5 |

| | |

| | |

| |Probability |

| |1/3 |

| |1/3 |

| |1/3 |

| | |

| | |

| |The probability that X is at least 4 is |

| |A) 0. B) 1/3. C) 9/20. D) 2/3. E) 1. |

|31. |A fourth-grade teacher gives homework every night in both mathematics and language arts. The time to complete the mathematics |

| |homework has a mean of 10 minutes and a standard deviation of 3 minutes. The time to complete the language arts assignment has a|

| |mean of 12 minutes and a standard deviation of 4 minutes. Assuming the times to complete homework assignments in math and |

| |language arts are independent, the standard deviation of the time required to complete the entire homework assignment is |

| |A) 16 minutes. B) 5 minutes. C) 4 minutes. D) 3 minutes. E) [pic]minutes. |

Chapter 8

|32. |A small class has 10 students. Five of the students are male and five are female. I write the name of each student on a 3-by-5 |

| |card. The cards are shuffled thoroughly and I choose one at random, observe the name of the student, and replace it in the set. |

| |The cards are thoroughly reshuffled and I again choose a card at random, observe the name, and replace it in the set. This is |

| |done a total of four times. Let X be the number of cards observed in these four trials with a name corresponding to a male |

| |student. The random variable X has which of the following probability distributions? |

|A) |The normal distribution with mean 2 and variance 1. |

|B) |The binomial distribution with parameters n = 4 and p = 0.5. |

|C) |The binomial distribution with parameters n = 4 and p = 0.1. |

|D) |The uniform distribution on 0, 1, 2, 3, and 4. |

|E) |None of the above. |

|33. |For which of the following counts would a binomial probability model be reasonable? |

|A) |The number of traffic tickets written by each police officer in a large city during one month. |

|B) |The number of hearts in a hand of five cards dealt from a standard deck of 52 cards that has been thoroughly shuffled. |

|C) |The number of 7’s in a randomly selected set of five random digits from a table of random digits. |

|D) |The number of phone calls received in a one-hour period. |

|E) |All of the above. |

|34. |A set of 10 cards consists of five red cards and five black cards. The cards are shuffled thoroughly and I choose one at random,|

| |observe its color, and replace it in the set. The cards are thoroughly reshuffled and I again choose a card at random, observe |

| |its color, and replace it in the set. This is done a total of four times. Let X be the number of red cards observed in these |

| |four trials. The mean of X is |

| |A) 4. B) 2. C) 1. D) 0.5. E) 0.1. |

|35. |A college basketball player makes 80% of his free throws. At the end of a game, his team is losing by two points. He is fouled |

| |attempting a three-point shot and is awarded three free throws. Assuming free throw attempts are independent, what is the |

| |probability that he makes at least two of the free throws? |

| |A) 0.896. B) 0.80. C) 0.64. D) 0.512. E) 0.384. |

Chapter 9

36. If a population has a standard deviation [pic], then the standard deviation of the mean of 100 randomly selected items from this population is

(a) [pic]

(b) 100 [pic]

(c) [pic]/10

(d) [pic]/100

(e) 0.1

37. The distribution of values taken by a statistic in all possible samples of the same size from the

same population is

(a) The probability that the statistic is obtained

(b) The population parameter

(c) The variance of the values

(d) The sampling distribution of the statistic

(e) None of the above.

38. If a statistic used to estimate a parameter is such that the mean of its sampling distribution is

equal to the true value of the parameter being estimated, the statistic is said to be

(a) Random

(b) Biased

(c) A proportion

(d) Unbiased

(e) None of the above.

39. A simple random sample of 1000 Americans found that 61% were satisfied with the service

provided by the dealer from which they bought their car. A simple random sample of 1000

Canadians found that 58% were satisfied with the service provided by the dealer from which they

bought their car. The sampling variability associated with these statistics is

a) Exactly the same.

b) Smaller for the sample of Canadians because the population of Canada is smaller than that of the United States, hence the sample is a larger proportion of the population.

c) Smaller for the sample of Canadians because the percentage satisfied was smaller than that for the Americans.

d) Larger for the Canadians because Canadian citizens are more widely dispersed throughout the country than in the United States, hence they have more variable views.

e) About the same.

40. The weights of 9 men have mean [pic] = 175 pounds and standard deviation s = 15 pounds. What is

the standard error of the mean?

(a) 58.3

(b) 19.4

(c) 5

(d) 1.7

(e) None of the above.

41. In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately

a) 0.03

b) 0.25

c) 0.0094

d) 6.12

e) 0.06

Chapter 10

41. You want to compute a 96% confidence interval for a population mean. Assume that the

population standard deviation is known to be 10 and the sample size is 50. The value of z* to be

used in this calculation is

(a) 1.960

(b) 1.645

(c) 1.7507

(d) 2.0537

(e) None of the above.

42. You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume that the population standard deviation is σ = 100. If you want the margin of error to be approximately 10, you will need a sample size of

(a) 16

(b) 271

(c) 38

(d) 1476

(e) None of the above.

43. You have measured the systolic blood pressure of a random sample of 25 employees of a

company located near you. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138). Which of the following statements gives a valid interpretation of this interval?

(a) Ninety-five percent of the sample of employees has a systolic blood pressure between 122 and 138.

(b) Ninety-five percent of the population of employees has a systolic blood pressure between 122 and 138.

(c) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

(d) The probability that the population mean blood pressure is between 122 and 138 is .95.

(e) If the procedure were repeated many times, 95% of the sample means would be between 122 and 138.

44. An analyst, using a random sample of n = 500 families, obtained a 90% confidence interval for mean monthly family income for a large population: ($600, $800). If the analyst had used a 99% confidence coefficient instead, the confidence interval would be:

a) Narrower and would involve a larger risk of being incorrect

b) Wider and would involve a smaller risk of being incorrect

c) Narrower and would involve a smaller risk of being incorrect

d) Wider and would involve a larger risk of being incorrect

e) Wider but it cannot be determined whether the risk of being incorrect would be larger or smaller

45. You want to design a study to estimate the proportion of students on your campus who agree with the statement, “The student government is an effective organization for expressing the needs of students to the administration.” You will use a 95% confidence interval and you would like the margin of error to be 0.05 or less. The minimum sample size required is approximately

a) 22

b) 1795

c) 385

d) 271

e) None of the above.

46. A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out he poses the following question to his listeners. “Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?” He asks listeners to phone in and vote “yes” if they agree the drinking age should be lowered and “no” if not. Of the 100 people who phoned in 70 answered “yes.” Which of the following conditions for inference about a proportion using a confidence interval are violated?

a) The data are an SRS from the population of interest.

b) The population is at least ten times as large as the sample.

c) n is so large that both the count of successes n p and the count of failures n(1 – p) are ten or more.

d) There appear to be no violations.

e) More than one condition is violated.

47. A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95% confidence margin of error of 3 %. This means that

(a) If the poll were conducted again in the same way, there is a 95% chance that the fraction of voters favoring term limits in the second poll would be between 61 % and 67 %.

(b) There is a 95% probability that the true percentage of voters favoring term limits is between 61 and 67%.

(c) If the poll were conducted again the same way, there is a 95% probability that the percentage of voters favoring term limits in the second poll would be within 3 % of the percentage favoring term limits in the first poll.

(d) Among 95% of the voters, between 61 % and 67 % favor term limits.

(e) None of the above.

Chapter 11/12

48. A significance test gives a P-value of 0.04. From this we can

(a) Reject H0 at the 1% significance level

(b) Reject H0 at the 5% significance level

(c) Say that the probability that H0 is false is 0.04

(d) Say that the probability that H0 is true is 0.04

(e) None of the above.

49. A significance test was performed to test the null hypothesis H0: µ = 2 versus the alternative

Ha: µ [pic] 2. The test statistic is z = 1.40. The P-value for this test is approximately

(a) 0.16

(b) 0.08

(c) 0.003

(d) 0.92

(e) None of the above.

50. In preparing to use a t procedure, suppose we were not sure if the population was normal. In which of the following circumstances would we not be safe using a t procedure?

(a) A stemplot of the data is roughly bell shaped.

(b) A histogram of the data shows moderate skewness.

(c) A stemplot of the data has a large outlier.

(d) The sample standard deviation is large.

(e) The t procedures are robust, so it is always safe.

51. What is the critical value t* that satisfies the condition that the t distribution with 8 degrees of freedom has probability 0.10 to the right of t*?

(a) 1.397

(b) 1.282

(c) 2.89

(d) 0.90

(e) None of the above.

52. Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are normally distributed with mean [pic]. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses

H0: [pic] = 14

Ha: [pic] < 14

53. To do this, he selects sixteen bags of this brand at random and determines the net weight of each. He finds the sample mean to be [pic]= 13.82 and the sample standard deviation to be s = 0.24.

We conclude that we would

f) Reject H0 at significance level 0.10 but not at 0.05.

g) Reject H0 at significance level 0.05 but not at 0.025.

h) Reject H0 at significance level 0.025 but not at 0.01.

i) Reject H0 at significance level 0.01.

j) Fail to reject H0 at the [pic] = 0.10 level.

54. An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are:

(a) [pic]

(b) [pic]

(c) [pic]

(d) [pic]

(e) None of the above.

Chapter 13

55. Suppose we have two SRSs from two distinct populations and the samples are independent. We measure the same variable for both samples. Suppose both populations of the values of these variables are normally distributed but the means and standard deviations are unknown. For purposes of comparing the two means, we use

(a) Two-sample t procedures

(b) Matched pairs t procedures

(c) z procedures

(d) The least-squares regression line

(e) None of the above.

56. Some researchers have conjectured that stem-pitting disease in peach tree seedlings might be controlled with weed and soil treatment. An experiment was conducted to compare peach tree seedling growth with soil and weeds treated with one of two herbicides. In a field containing 20 seedlings, 10 were randomly selected from throughout the field and assigned to receive Herbicide A. The remaining 10 seedlings were to receive Herbicide B. Soil and weeds for each seedling were treated with the appropriate herbicide, and at the end of the study period, the height (in centimeters) was recorded for each seedling. A box plot of each data set showed no indication of non-normality. The following results were obtained:

|Herbicide A: |[pic]1 = 94.5 cm |s1 = 10 cm |

|Herbicide B: |[pic]2 = 109.1 cm |s2 = 9 cm |

|Suppose we wished to determine if there tended to be a significant difference in mean height for the seedlings treated with the |

|different herbicides. To answer this question, we decide to test the hypotheses H0: μ2 – μ1 = 0, Ha: μ2 – μ1 ≠ 0. Based on our |

|data, the value of the two-sample t test statistic is |

|A) 14.60. B) 7.80. C) 3.43. D) 2.54. E) 1.14. |

| |

| |

|Use the following information for #57 and 58. |

A researcher wished to test the effect of the addition of extra calcium to yogurt on the “tastiness” of yogurt. A collection of 200 adult volunteers was randomly divided into two groups of 100 subjects each. Group 1 tasted yogurt containing the extra calcium. Group 2 tasted yogurt from the same batch as group 1 but without the added calcium. Both groups rated the flavor on a scale of 1 to 10, with 1 being “very unpleasant” and 10 being “very pleasant.” The mean rating for group 1 was [pic]1 = 6.5 with a standard deviation of s1 = 1.5. The mean rating for group 2 was [pic]2 = 7.0 with a standard deviation of s2 = 2.0. Assume the two groups’ ratings are independent. Let μ1 and μ2 represent the mean ratings we would observe for the entire population represented by the volunteers if all members of this population tasted, respectively, the yogurt with and without the added calcium.

|57. |Suppose the researcher had wished to test the hypotheses H0: μ1 = μ2, Ha: μ1 < μ2. The P-value for the test (using the |

| |conservative value for the degrees of freedom) is |

|A) |larger than 0.10. |D) |between 0.001 and 0.01. |

|B) |between 0.05 and 0.10. |E) |below 0.001. |

|C) |between 0.01 and 0.05. | | |

|58. If we had used the more accurate software approximation to the degrees of freedom, we would have used which of the |

|following as the number of degrees of freedom for the t procedures? |

| A) 16. B) 14. C) 12. D) 9. E) 8. |

| |

Chapter 14

Use the following information for # 59 and 60.

Using computer software, I generate 1000 random numbers that are supposed to follow a standard normal distribution. I classify these 1000 numbers according to whether their values are less than –2 (value < –2), between –2 and 0 (–2 ≤ value < 0), between 0 and 2 (0 ≤ value < 2), or at least 2 (value ≥ 2). The results are given in the following table. The expected counts are computed using the 68–95–99.7 rule.

| |Less than |Between |Between |At least |

| |–2 |–2 and 0 |0 and 2 |2 |

|Observed count |18 |492 |468 |22 |

|Expected count |25 |475 |475 |25 |

To test to see if the distribution of observed counts differs significantly from the distribution of expected counts, we use the χ2 statistic.

|59. |In this case, the χ2 statistic has approximately a chi-square (χ2) distribution. How many degrees of freedom does this |

| |distribution have? |

| |A) 3. B) 4. C) 7. D) 999. E) 1000. |

|60. Which of the following statements is true of chi-square distributions? |

|A) |They take on only positive values. |

|B) |Their density curves are skewed to the left. |

|C) |As the number of degrees of freedom increases, their density curves look more and more like a uniform distribution. |

|D) |As the number of degrees of freedom increases, their density curves look less and less like a normal curve. |

|E) |All of the above. |

Use the following information for # 61 and 62.

A professor teaches a large introductory statistics course. In the past, the proportions of students that received grades of A, B, C, D, or F have been, respectively, 0.20, 0.30, 0.30, 0.10, and 0.10. This year, there were 200 students in the class, and I gave them the following grades.

|Grade |A |B |C |D |F |

|Number |56 |74 |60 |9 |1 |

He wishes to test to see whether the distribution of grades this year was different from the distribution in the past. To do so, I plan to use the χ2 statistic.

|61. Assuming that the χ2 statistic has approximately a χ2 distribution, how many degrees of freedom does the distribution have?|

| A) 200. B) 199. C) 9. D) 5. E) 4. |

|62. The grade category that contributes the largest component to the χ2 statistic is |

| A) A. B) B. C) C. D) D. E) F. |

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download