AP Stat Test Prep

Which of the following is the best estimate of the standard deviation of the distribution showin in the figure above? (figure looks like a mountain and starts at about 20 and ends at about 80 but diagram only shows the numbers underneath of 30-70 in intervals of 10)

10

A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company's claim is correct, what is the expected number of nondefective lightbulbs in a random sample of 1,000 bulbs?

980

Which of the following can be used to show a cause-and-effect relationship between two variables?

A controlled experiment.

A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $127.95 and a standard deviation of $24.03. If the size of this sample is 40, which of the following is an approximate 90 percent confidence interval for the average cost of a repair at this repair shop?

$127.95(+−) $6.25

Ths XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as well as individually at retail prices. Next year's sales depend on market conditions, but executives use probability to find estimates of sales for the coming year. The following tables are estimates for next year's sales. Wholesale Sales....Numbers Sold (NS) 2,000/ Probability (Prob) 0.1....NS 5,000/Prob 0.3......NS 10,000/Prob 0.4.....NS 20,000/Prob 0.2 Retails Sales......NS 600/Prob 0.4.....NS 1,000/ Prob 0.5....NS 1,500/Prob 0.1 What profit does XYZ Office Supplies Company expect to make for the next year if the profit from each calculator sole is $20 at wholesale and $30 at retail?

$220,700

Every Thursday, Matt and Dave's Video Venture has "roll-the dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. First question on this scenario: If a customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies?

$9.40

Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. In this batch of chips, 90 percent of the chips are acceptable. Let X denote the number of acceptable chips out of a sample of 4 chips from this batch. What is the least probable value of X?

0

The process of producing pain-reliever tablets yields tables with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The mean content of the active ingredient for this sample is 194.3 milligrams, while the standard deviation is 21 milligrams. What is the appoximate p-value for the appropriate test?

0.012

Joe and Matthew plan to visit a bookstore. Based on their previous visits to this bookstore, the probability distributions of the number of books they will buy are given below..... Number of books Joe will buy/Probability...... 0/.50 1/.25 2/.25 Number of books Matthew will buy/Probability.....0/.25 1/.50 2/.25 Assuming that Joe and Matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore?

0.1250

Every Thursday, Matt and Dave's Video Venture has "roll-the dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. Second question on this scenario: If a customer rolls the dice and rents a movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00?

0.14

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model.... y=25.2 + 3.3x 9<x<25, where x is the number of chirps per minute and y is the estimated temperature in degress Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?

16.5°F

A 95 percent confidence interval of the form p(plus or minus)E will be used to obtain an estimate for an unknown population proportion p. If p is the sample proportion and E is the margin of error, which of the following is the smallest sample size that will guarantee a margin of error of at most 0.08?

175

The equation of the least squares regression line fror the points on the scatterplot above (could not include pictures but points are at 1,1/4,2/3,5/4,7/6,4/7,7) y=1.3 + 0.73x/ What is the residual for the point (4,7)?

2.78

A survey was conducted to determine what percentage of college seniors would have chosen to attend a different college if they had known what they know now. In a random sample of 100 seniors, 34 percent indicated that they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who would have attended a different college is

26.2% tp 41.8%

A magazine has 1,620,000 subscribers, of whom 640,000 are women and 980,000 are men. Thirty percent ofthe women read the advertisements in the magazine and 50 percent of the men read the advertisements in the magazine. A random sample of 100 subscribers is selected. What is the expected number of subscribers in the sample who read the advertisements?

42

When a virus is placed on a tobacco leaf, small lesions appear on the leaf. To compare the mean number of lesions produced by two different strains of virus, one strain is applied to half of each of 8 tobacco leaves, and the other strain is applied to the other half of each leaf. The strain that goes on the right half of the leaf is decided by a coin flip. The lesions that appear on each half are then counted. The data are given below: Leaf 1/ Strain 1=31/ Strain 2=18.......Leaf 2/20/17....Leaf 3/18/14....Leaf 4/17/11...Leaf 5/9/10....Leaf 6/8/7....Leaf 7/10/5....Leaf 8/7/6....What is the number of degress of freedom associated with the appropriate t-test for testing to see if there is a difference between the mean number of lesions per leaf produced by the two strains?

7

The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is closest to

70

A certain county has 1,000 farms. Corn is grown on 100 of these farms but on none of the others. In order to estimate the total farm acreage of corn for the county, two plans are proposed. Plan I: (a) Sample 20 farms at random. (b) Estimate the mean acreage of corn per farm in a confidence interval. (c) Multiply both ends of the interval by 1,000 to get an interval estimate of the total. Plan II: (a) Identify the 100 corn-growing farms. (b) Sample 20 corn-growing farms at random (c) Estimate the mean acreage of corn for corn-growing farms in a confidence interval (d) Multiply both ends of the interval by 100 to get an inteval estimate of the total. On the basis of the information given, which of the following is the better method for estimating the total farm acreage of corn for the county?

Choose plan II over plan I.

Ten students were randomly selected from a high school to take part in a program designed to raise their reading comprehension. Each student took a test before and after completing the program. The mean of the differences between the score after the program and the score before the program is 16. Its was decided that all studens in the school would take part in this program during the next school year. Let µ(A) denote the mean score after the program and µ(B) denote the mean score before the program for all students in the school. The 95 percent confidence interval estimate of the true mean difference for all students is (9,23). Which of the following statements is a correct interpretation of this confidence interval?

For any µ(A) and µ(B) with 9<(µ(A)-µ(B)<23, the sample result is quite likely

Gina's doctor told her that the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.50. Which of the following is the best interpretation of this standardized score?

Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age

An automobile manufacturer claims that the average gas mileage of a new model is 35 miles per gallon (mpg). A consumer group is skeptical of this claim and thinks the manufacturer may be overstating the average gas mileage. If µ represents the true average gas mileage for this new model, which of the following gives the null and alternative hypotheses that the consumber group should test?

H₀: µ= 35 mpg Hα: u< 35 mpg

The Physicians' Health Study, a large medical experiment involving 22,000 male physicians, attemped to determine whether aspirin could help prevent heart attacks. In this study, one group of about 11,000 physicians took an aspirin every other day, while a control group took a placebo. After several years, it was determined that the physicians in the group that took aspirin had significantly fewer heart attacks that the physicians in the control group. Which of the following statements explains why it would NOT be appropriate to say that everyone should take an aspirin every other day?

I,II, and III....which are "The study included only physicians, and different results may occur in individuals in other occupations"...."The study included only males and there may be different results for females"..."Although taking aspirin may be helpful in preventing heart attacks, it may be harmful to some other aspects of health"

The boxplots above (picture not included but Set A is a little larger going from about 21-39 and a line in the middle at 30....and Set B goes from about 22-38 and a line a little left of middle at 29) summarize two data sets, A and B. Which of the following must be true?

III only-- which is "The data in Set A have a larger range that the data in Set B"

A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correcting was made?

Median

To check the effect of cold temperature on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a freezer for two hours and ten bands from the Brand B box are kept at room temperture. The amount of stretch before breakage is measured on each rubber band, and the mean for the cold bands is compared to the mean for the others. Is this a good experimental design?

No, because temperature is confounded with brand.

The student government at a high school wants to conduct a survey of student opinion. It wants to begin with a simple random sample of 60 students. Which of the following survey methods will produce a simple random sample?

Number the students in the official school roster. Use a table or random numbers to choose 60 students from this roster for the survey.

USA Today reported that speed skater Bonnie Blair had "won the USA's heart," according to a USA Today/Cnn/Gallup poll conducted on the final Thursday of the 1994 Winter Olympics. When asked who was the hero of the olympics, 65 percent of the respondents chose Blair who won five gold medals. The poll of 615 adults, done by telephone, had a margin of error of 4 percent. Which of the following statements best describes what is meant by the 4 percent margin of error?

The difference between the sample percentage and the population percentage is likely to be less than 4 percent.

The back-to-back stem-and-leaf plot below (can't include the actual plot) gives the percentage of students who dropped out of school at each of the 49 high schools in a large metropolitan school district. Which of the following statements is NOT justified by these data?

The drop-out rate decreased in each of the 49 high schools between the 1989-1990 and 1992-1993 school years

Which of the following is a criterion for choosing a t-test rather than a z-test when making an inference about the mean of a population?

The standard deviation of the population is unknown

At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores ont eh calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the chemistry final and 84 on the calculus final. Relative to the students in each respective class, in which subject did this student do better?

The student did equally well in each course.

Chart: Juniors / Job 13/ No Job 5/ Total 18...... Seniors/ Job 13/ No Job 26/ Total 39..... Total/ Job 26/ No Job 31/ Total 57 A survey of 57 students was conducted to determine whether or not they held jobs outside of school. The two-way table above shows the numbers of students by employment status (job, no job) and class (juniors, seniors). Which of the following best describes the relationship between employment status and class?

There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs.

In a test of the null hypothesis H₀: µ=10 against the alternative hypothesis H(a): µ>10, a sample from a normal population produces a mean of 13.4. The z-score for the sample is 2.12 and the p-value is 0.017. Based on these statistics, which of the following conclusions could be drawn?

There is reason to conclude that µ>10.

For which of the following distributions is the mean greater that the median?

answer is a picture....description of picture as follows: sloped line going down from y-axis to x-axis

A fair coin is flipped 10 times and the number of heads is counted. The procedure of 10 coin flips is repeated 100 times and the results are place in a frequency table. Which of the frequency tables below is most likely to contain the results from these 100 trials?

chart shows number of heads 0-10 and then the following frequencies in order.... 0/0/6/9/22/24/18/12/7/2/0 (REMEMBER two zeros at top and just 1 zero at end)

The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10 percent of the loaves wighed les than 15.34 ounces, and 20 percent of the loaves weighed more than 16.31 ounces. What are the mean and standard deviation of the distribution of the weights of the loaves of bread?

µ=15.93, δ=0.46