6.02 Quiz: AP-Style Multiple-Choice Questions, Part 2
Teachers in a medium-sized suburban school district have an average salary of $47,500 per year, with a standard deviation of $4,600. After negotiating with the school district, teachers receive a 5% raise and a one-time $500 bonus. What are the new mean and standard deviation of the teacher's salaries during the year in which they receive the bonus?
$50,375; $4,830
Assuming that this regression was based on a sample of several hundred individuals, a 95% confidence interval for the slope of the regression line would be given by:
.0385 ± 1.96(.0728)
You have a rather strange letter cube: Three faces are marked with the letter A, two faces with the letter B, and one face with the letter C. You roll the letter cube until you get a B. What is the probability that a B does not appear during the first three rolls?
.296
Leroy and Fred play chess at a club every Wednesday. The probability that Leroy will lose is .3, that he will stalemate is .5, and that he will win is .2. The probability that Fred will lose is .25, that he will stalemate is .4, and that he will win is .35. What is the probability that at least one of them wins on a given Wednesday?
.48
A manufacturer claims that the batteries it makes will last 18 hours, with a standard deviation of 1.5 hours. If the durations of the batteries are normally distributed, what proportion of batteries would be expected to last less than 16 hours?
0.0918
Which of the following statements are true? 1. Boxplot A has a greater range than boxplot B. 2. Boxplot A has a smaller IQR than boxplot B. 3. Boxplot B contains more data than boxplot A.
1 and 2 only
To use a t procedure, which of the following must be true? 1. The standard deviation of the parent population must be unknown. 2. The sample size must be small (less than 30). 3. The parent population must be normally distributed.
1 and 3 only
Given the tree diagram above, what is P(A | C)?
17/27
Which of the following statements is true of hypothesis testing? 1. You must always state a significance level when doing a hypothesis test unless you are using a confidence interval. 2. To say a finding is significant means that it is unlikely to have occurred by chance. 3. A confidence interval can be used as evidence in a two-sided hypothesis test.
2 and 3 only
To determine the health benefits of walking, researchers conduct a study in which they compare the cholesterol levels of women who walk at least 10 miles per week to those of women who do not exercise at all. The study finds that the average cholesterol level for the walkers is 198, and that the level for those who don't exercise is 223. Which of the following statements is true? 1. This study provides good evidence that walking is effective in controlling cholesterol. 2. This is an observational study, not an experiment. 3. Although the study was conducted only on women, we can confidently generalize the results to men in the same age group.
2 only
A school designs two experimental courses (course A and course B) and randomly assigns 50 students so that there are 25 in each course. At the end of the year, the average final exam score in course A was 75 with a standard deviation of 7, and in course B it was 72 with a standard deviation of 5. Which of the following gives a 99% confidence interval for the difference between the final exam scores of course A and course B?
3 ± 2.797 √7²/25 + 5²/25
Which of the following is the best estimate of the standard deviation of the normal distribution shown here?
4
The weight of adult Golden Retrievers is normally distributed with a mean of 65 lb and a standard deviation of 3 lb. A random sample of 15 Golden Retrievers has an average weight of 66 lb. The percentile rank of this sample is:
90
To test a new diet drug, researchers divide their 96 subjects by gender into two groups (there are equal numbers of men and women). They then randomly subdivide these into three groups each so they can test three different dosages. Which of the following best describes the design of this experiment?
A comparative randomized design, blocked by gender.
Which of the following is not a necessary component of a valid experimental design?
Blocking.
Given the linear regression analysis above, which of the following conclusions can we draw?
It is unlikely that the slope of the regression line is different from zero.
In a recent public opinion poll of 750 adults, 40% said that, if they had to decide between watching a rerun of Gilligan's Island and watching the State of the Union address, they'd choose the rerun. The poll reported a margin of error of 5%. Which of the following best describes what is meant by a 5% margin of error?
The true population percentage is likely to be within 5% of the sample percentage.
In an experiment, the purpose of randomizaton is to:
equalize treatment groups.
We have a null hypothesis that mu = 3.75, but we are reluctant to accept this as the population value in case the true value is different. An analysis tells us that the probability of rejecting the null hypothesis, if mu is really 3.95, is .75. This probability is:
the power of the test against the alternative mu = 3.95.
In a fund-raising game for your school, you bet $1 to roll two number cubes. If your total is 8, 9, 10, or 11, you win $2. If your total is 12, you win $6. If your total is 7 or less, you lose the dollar you bet. How much, on average, do you expect to win or lose with each dollar bet?
You will lose 5.6 cents.
