AP Stats Midterm: Ch. 1 - 6

A ride-sharing company claims that the cost of rides follows Normal distribution with a mean of $10.52. After paying for a ride from this company, a rider reports that his prices is in the 85th percentile of all other riders' prices. If this rider paid $15.93, what is the approximate standard deviation of this company's ride-sharing cost.

$5.20

Karen is playing a board game in which she rolls a fair six-sided number cube until she rolls a six. One she rolls a six, she can advance her piece on the board. What is the probability that the first six Karen rolls is on her fifth roll?

(5/6)^4 (1/6)

A teacher decides to play a game to collect homework. Each day, when students walk into class, they select a token from a bag that contains red and gold tokens. If the token they select is gold, the student will not have to turn in their homework. The teacher tells the class that there is a 30% chance of selecting a gold token. The students pull a token all five days in one week. Which of the following correctly represents the probability that a student will not have to turn in homework exactly two times?

(^5 2) (0.3)^2 (0.7)^3

The cost of items at store A is approximately Normally distributed with a mean of $4.15 and a standard deviation of $2.68. The cost of items at store B is approximately Normally distributed with a mean of $5.35 and a standard deviation of $1.75. Assume that A (the cost of a randomly selected item from store A) and B (the cost of a randomly selected item from store B) are independent variables. Let D= A-B. Which of the following correctly interprets the mean of D?

-$1.20. On average, a person can expect to spend $1.20 less at store A than at store B for many randomly chosen items.

The probability that a student will receive a state grant is 0.32, while the probability that a student will be awarded a federal grant is 0.45. If whether a student receives one grant is not influenced by whether student receives the other, what is the probability of a student receiving both grants?

.144

The area under the standard normal curve corresponding to -0.3<Z<1.6 is

.5631

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean $360 and standard deviation $50. What is P(X > $400)?

0.2119

A fire department in a rural county reports that its response time to fires is approximately Normally distributed with a mean of 22 minutes and a standard deviation if 11.9 minutes. Approximately what proportion of their response time is over 30 minutes?

0.25

From many years of fishing, Carlos knows that his probability of catching a fish on any given day is 0.65. Suppose that he plans on fishing all seven says next week. What is the probability that he catches fish on exactly four of those days?

0.268

For two independent events A and B, P(A) = 0.4 and P(B) = 0.15. What is P(A or B)?

0.49

The number of shoes a group of college students own is approximately Normally distributed with a mean of 22.1 and a standard deviation of 6.3. About what proportion of the students own between 20 and 30 pairs of shoes?

0.5256

Here are the IQ scores of 10 randomly chosen fifth-grade students: 145, 139, 126, 122, 125, 130, 96, 110, 118, 118 To make a stemplot of these scores you would use at stems

09, 10, 11, 12, 13 and 14

The cumulative frequency graph at right shows the distribution of lengths (in centimeters) of fingerlings at a fish hatchery. The interquartile range for this distribution is

1.2 centimeters

A medical research team collects health data on many women in each of several countries .One of the variables measured for each women in the study is her weight in pounds. The following list gives the five-number summery for the weights of adult women in one of the countries. Country A: 92, 110, 120, 160, 240 About what percent of Country A women weigh between 110 and 240 pounds?

75%

The stemplot below shows how many kernels of popcorn actually popped per bag of a certain microwave brand of popcorn. Natalie's bag popped 157 kernels. What is the percentile of the number of kernels popped for her bag of popcorn?

85th percentile

A nutritionist wants to study the effect of storage time (6, 12, and 18 months) on the amount of vitamin C present in freeze dried fruit when stored for these lengths of time. Vitamin C is measured in milligrams per 100 milligrams of fruit. Six fruit packs were randomly assigned to each of the three storage times. The treatment, experimental unit, and response are respectively:

A specific storage time, a fruit pack, amount of vitamin C

The two-way table below gives information on the performers in the New York Philharmonic Orchestra, categorized by section (type of instrument) and gender. A. You select one musician from this group at random, What is the probability that this person plays a woodwind? B. You select one musician from this group at random. If the person is a male, what is the probability that he plays a woodwind? C. You select one musician from this group at random. Which of the following statements is true about the events "Plays a woodwind" and "Male?"

A. 0.159 B. 0.182 C. The events are not mutually exclusive, nor are they independent

On May 7, 1915, a German U-boat sank the British ocean liner RMS Lusitania. The table below shows the summary of the passengers aboard the ship (excluding crew) and whether they survived or died in the attack. A. What percent of passengers survived the attack? B. What percent of the second-cabin passengers on the RMS Lusitania survived the attack?

A. 476/ 1261 = 37.7% B. 229/ 601 = 38.1%

The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. A. Only about 5% of young men have heights outside the range: B. About what percentage of the men are over 70.5 inches tall?

A. 63 inches to 73 inches B. 16

In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation was y hat = 10 + 0.9x where y is the final-exam score and x is the score on the first test. A. Betsy scored 95 on her the test. What is the predicted value of her score on the final exam? B. Kurt scored a 90 on the first test and a 93 on the final exam. What is the value of his residual?

A. 95.5 B. 2.0

One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: A. The least squares regression line is the line that B. Which of the following is correct?

A. minimizes the sum of the squared residuals between the actual yield and the predicted yield. B. If the UV value increases by 1 Dobson unit, the yield is expected to decrease by 0.0463.

Consider the following studies being run by three different nursing home establishments. I.One nursing home has pets brought in for an hour every day to see if patient morale is improved. II.One nursing home allows hourly visits every day by kindergarten children to see if patient morale is improved. III.One nursing home administers antidepressants to all patients to see if patient morale is improved. Which of the following is true?

All of the above

The Normal probability plot below shows data on the weights of Labrador retrievers. What conclusions can be made about Normality from this plot?

Because of the linear pattern in the probability plot, we can conclude that the weights of Labrador retrievers are approximately Normal.

The heights, in inches, of 100 young adults were recorded and used to create the histogram below. Which of the following is a correct statement?

Because the graph is roughly symmetric, the mean and median should be approximately equal.

Which statements below about the least square regression are correct? I. Switching the explanatory and response variables will not change the least square regression line. II. The slope of the line is very sensitive to outliers with large residuals. III. A value of r^2 close to 1 does not guarantee that the relationship between the variables is linear.

Both II and III

Which of the following are important in the design of an experiment? I. Control of confounding variables II. Randomization in assigning subjects to different treatments III. Replication if the experiment using sufficient numbers of subjects

I, II, III

Which of the following are true statements? I. In an experiment some treatment is intentionally forced on one group to note the response. II. In an observational study information is gathered on an already existing situation. III. Sample surveys are observational studies, not experiments.

I, II, and III

A set of data describes the relationship between the size of annual salary raises and the performance rating for employees of a certain company. The least squares regression equation is y=1400 + 2000x where y is the raised amount (in dollars) and x is the performance rating. Which of the following statements must be true?

If the mean performance rating is 1.2, the the mean raise is $3800.

In the science club at school, 22 of the students have pets and 25 do not. In a sample of 10 students from the club, only one of them had a pet. The students want to do a simulation to determine if such a sample is unusual. Which of the following statements describes how the students could use a table of random digits to carry out this simulation?

Label the students with pets 01-22 and the students without pets 23-47. Reading the random digit table from left to right, ignoring repeated values and numbers 48-99 and 00, select digits two at a time until 10 students numbers have been selected.

The receipts at a grocery store show the total number of items each customer purchased. Some of the receipts showed these results: 17, 19, 22, 38, 38, 45, 46, 47, 48, 50, 52, 51, 56, and 73. Which of the following is the median with its correct interpretation?

Median = 46.5; about 50% of shoppers at this store will buy fewer than 46.5 items.

Rainwater was collected in water collectors at 30 different sites near an industrial complex and the amount of acidity (pH level) was measured. The data ranged from pH 2.6 to pH 6.3. The following stemplot of the data was constructed. Which of the following boxplots is a correct representation of the same distribution?

Min: 2.6 Q1: 3.8 Med: 4.5 Q3: 5.6 Max: 6.3

Dwayne has collected data on the number of occupants of cars traveling on the road past his house for the past week. Based on his data, he has constructed a probability model for the number of occupants of a randomly-selected car on his street. Which of the following could be his model?

No. I Prob 1 I 0.10 2 I 0.11 3 I 0.25 4 I 0.05 5 I 0.26

Which of the following statements is true? (about nonresponse bias)

Nonresponse can cause bias in surveys because nonrespondents may behave differently than people who respond

A researcher for a consumer products company is field testing a new formula for laundry detergent. He has contracted with 60 families, each with 2 children, who have agreed to test the product. He randomly assigns 30 families to the group that will use the new formula and 30 to the group that will use the company's current detergent formula. The most important reason for this assignment is

Randomization is a good way to create 2 groups of 30 families that are as similar as possible, so that comparisons can be made between the 2 groups

Control groups are used in experiments in order to accomplish which one of the following

Reduce the variability in results

The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times is

Skewed to the right, with mean 0 and standard deviation 1.

A statistics student wanted to determine if the distance to a destination was related to the price an airline would charge to fly to that destination. The student did a regression of Airfare (y) on Distance (x) and obtained the printout shown from a statistical software package. Which of the following correctly interprets the value of 25.25?

The actual prices will vary by about $25.25 of the price predicted for their distance by the linear model.

For the density curve shown to the right, which statement is true?

The area under the curve between 0 and 1 is 1.

A researcher observes that, on average, the number of divorces in cities with Major League Baseball teams is larger than in cities without Major League Baseball teams. Which of the following is the most plausible explanation for this observed association?

The association is due to confounding (Major League teams tend to be in large cities with more people, hence a greater number of divorces)

All but one of the following statements contains an error. Which statement could be correct?

The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r=0.53.

The scatterplot below shows the model year, x, and the asking price, y, of cars of a particular model on a used car website. There is one car at the point (1989, 3475). Suppose the data set had been presented without this car included. What effect would this point's absence have on the correlation coefficient?

The correlation would increase.

A least-squares regression line for predicting weights of basketball players on the basis of their heights produced the residual plot below. What does the residual plot tell you about the linear model?

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

The mean birth weight of infants born at a certain hospital in the month of April was 128 oz. with a standard deviation of 10.2 oz. Which of the following is the correct interpretation of the standard deviation?

The distance between the weight of each infant born in April and the mean weight was, on average, about 10.2.

The graph at the right 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?

The distribution is skewed right.

If a distribution is skewed to the right, which of the following is true

The mean must be greater than the median

A small company that prints custom t-shirts has 6 employees, one of whom is the owner and manager. Suppose the owner makes $120,000 per year and the other employees make between $40,000 and $50,000 per year. One day, the owner decided to give himself a $30,000 raise. Which of the following describes how the company's mean and median salaries would change?

The mean would increase by $5000 and the median would not change.

The number of copies made each week by teachers at Lamely high school follows a bell-shaped distribution with a mean of 550 copies and a standard deviation of 185 copies. Mr. Thomas made 782 copies last week. His z-score is 1.25. Which of the following statements best interprets this value?

The number of copies Mr. Thomas made is 1.25 standard deviations more than the mean number of copies of teachers at Lamely High School.

In order for the random variable X to have a geometric distribution, which of the following conditions must X satisfy?

The probability of success has to be the same for each trial.

A sample of 250 high school students were asked "If you had $1000 to contribute to one kind of charitable organization, which type of organization would you choose?"

The proportion of males who said they would contribute to an environmental organization was higher than the population of females who said they would contribute such an organization

In order to attract more customers to the restaurant and earn more revenue, a restaurant manager mails out coupons for 10% off the entire bill, valid only on Tuesdays. Describe what happens to the shape, center, and spread of the distribution of the restaurant's revenue on Tuesdays after the 10% discount is given.

The shape remains the same, but the center and spread both decrease by 10%.

The pie chart at right describes the distribution of state trees for the 50 states in the US. The category "other" includes all trees that are the state tree for two or fewer states. Which of the following conclusions can we draw from this chart?

There are 10 states that have designated a pine as their state tree

A consumer product agency tests miles per gallon for a sample of automobiles using each of four different octanes of gasoline. Which of the following is true?

There are four levels of a single explanatory variable.

The following bar graph gives the percent of owners of three brands of truck owners who are satisfied with their truck. From this graph, we may conclude that

There are only small differences in the satisfaction of owners for the three brands

An ice cream shop keeps track of how many customers come in daily. The table of numerical summaries below has the information that was collected last month. Which of the following must be true?

There is at least one outlier on the high end.

Eighty volunteers who currently use a certain brand of over-the-counter allergy medication have been recruited to participate in a trial of a new allergy medication. The volunteers are randomly assigned to one of two groups. One group continues to take their current medication, the other group switches to the new experimental medication. Each is asked after two weeks if their allergy symptoms are worse, better, or about the same as they were at the start of the study. Which of the follow best describes a conclusion that can be drawn from this study?

We can determine whether the new drug reduces symptoms more than the old drug for the subjects in the study.

A survey is to be administered to recent graduates of a certain nursing school in order to compare the starting salaries of women and men. For a random sample of graduates, three variables are to be recorded: sex, starting salary, and area of specialization. Which of the follow best describes a conclusion that can be drawn from this study?

Whether there is an association between sex and starting salary among graduates of this nursing school.

What electrical changes occur in muscles as they get tired? Student subjects are instructed to hold their arms above their shoulders as long as they can. Meanwhile, the electrical activity in their arm muscles is measured. This is

an uncontrolled experiment

A maple sugar manufacturer wants to estimate the average trunk diameter of sugar maples trees in a large forest. There are too many trees to list them all and take an SRS, so he divides the forest into several hundred 10 meter by 10 meter plots, selects 25 plots of random, and measures the diameter of every sugar maple each one. This is an example of a

cluster sample.

Other things being equal, larger automobile engines consume more fuel. You are planning an experiment to study the effect of engine size (in liters) on the gas mileage (in miles per gallon) of sport utility. (variables / correlation)

gas mileage is a response variable, and you expect to find a negative association.

We wish to draw a sample of 5 without replacement from a population of 50 households. Suppose the households are numbered 01, 02,.....,50, and suppose that the relevant line of the random number table is 11362 35692 96237 90842 46843 62719 64049 17823. Then the households selected are

households 11 36 23 08 42

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is:

mean= 2; standard deviation = 1.265

A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be —1 .08. On the basis of this you would tell the college that

the college should hire a new statistician.

The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

unchanged: equal to 0.52

An agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. This means that

when corn prices are above average, soybean prices also tend to be above average.