AP Stats Final
An efficiency consultant determines that on the assembly line at Widget Manufacturing, there is a strong, negative, linear relationship between x-the consecutive hours a worker has been assembling widgets and y=the number of widgets he can produce in an hour. He finds that 70% of the variability in widgets produced per hour can be explained by the least squares regression line. Which of the following is the best approximation of the correlation of x and y?
-0.84
A company produces packets of soap powder labeled "Giant size 32 ounces". The actual weight of the soap powder box has a normal distribution with a mean of 33 ounces and a standard deviation of 0.8 oz. What proportion of packet are underweight?
0.106
Birthweights at a local hospital have a normal distribution with the mean of 110 oz. and a standard deviation of 15 oz. Which of the following is the proportion of infants with birthweights between 125 oz. and 140 oz
0.135
The area under the standard Normal curve corresponding to -0.3 < Z < 1.6 is closest to what value?
0.5631
A consumer group surveyed the prices for a certain item in five different stores, and reported the average price as $15. We visited four of the five stores, and found the prices to be $10, $15, $15, and $25. Assuming that the consumer group is correct, what is the price of the item at the store that we did not visit?
10
For this density curve, what percent of the observations lie between x = 0.2 and x = 3.8
10 percent
the heights of american men aged 18 to 24 approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. About what percentage of the men are over 70.5 inches tall?
16
Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. The percent of bags that will contain between 16.0 and 16.1 ounces is about?
16 percent
Which statements below about least-squares regression are correct? 1. Switching the explanatory and response variables will NOT change the equation of the least-squares regression line. 2. the slope of the line is very sensitive to high leverage points with large residuals 3. a value of r^2 close to 1 does NOT guarantee that the relationship between the variables is linear
2 and 3 are correct
Here are the exam scores for the 14 students in Mrs. Gopaul's Statistics Class: 60 61 61 65 72 75 75 78 81 81 85 89 91 98 What is the percentile of the person whose score was 65?
28.6 percent
You measure the age (years), weight (pounds), and marital status (single, married, divorced, or widowed) of 1400 women. How many variables did you measure?
3
A 5 number summary for the lengths of the first 100 words in Robert Fagles' translation of Homer's Odyssey is 2,3,4,5, and 12. Which one of the following could be the 60th percentile of this distribution?
4
A researcher wishes to study how the average weight (in kilograms) of children changes during the first year of life. He plots these averages versus the age x (in months) and decides to fit least-squares regression line to the data with x as the explanatory variable and y as the response variable. He computes the following.
4.65
The five-number summary of test scores for the 600 students in Mrs. Hughes's Statistics class in Providence School is 52, 65, 78, 85, and 96. How many students scored higher than 65?
450
The pie chart at right describes the distribution of favorite school subjects for 300 high school students. How many students reported that "Math" is their favorite subject?
78
A linear regression equation was computed to predict the final-exam score in a statistics class from the score on the first test. The equation was y=10+0.9x where y was the final exam score and x is the score on the first test. Carla scored a 95 on the first test. What is the predicted value of her score on the final exam?
95.5
For the histogram below, what are the correct locations of the mean and median? Note that the graph is NOT numerically precise only the relative positions are important.
Il is the mean and III is the median.
The eight teachers listed below all teach statistics. 1. Rosales 2. Mann 3. Preble 4. Knaggs 5. Temple. 6. Boles 7. Kindred. 8.Chauvet Starting at the beginning of the random number list below, choose a simple random sample of four teachers to be given a raise. Use the labels attached to the eight names. 41842 81868 71035 09001 43367 49497 54580 81507
Rosales, Mann, Knaggs, and Chauvet.
The plot shown below is a normal probability plot for the total annual cost (tuition plus room and board) to attend 126 of the top colleges in the country in 2005. which statement is true for this distribution?
The distribution is clearly skewed to the left
The time it takes people to finish a certain kind of puzzle is strongly skewed to the right. Which of the following statements is true about the mean and median of this distribution?
The mean will be greater than the median
Shown below are box plots describing the distribution of prices paid for homes in two suburbs of Columbus, Ohio over a single 30-day period in 2016. Which of the following statements is supported by the information in this graph?
The median house price in Dublin is higher than the 75th percentile of house price in Westerville
A recent investigation of prices for five-year-old Toyota Camry's in Montgomery, Alabama and New York, New York, revealed that the mean price in Montgomery was $13,200 with a standard deviation of $1,000. In New York, the mean price was $12,800 with a standard deviation of $1,800. Which of the following statements are true?
The standardized score for a car price at $15,000 would be higher in Montgomery than in New York
Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side effect of drowsiness. To investigate this question, the researchers randomly assigned 100 adult volunteers who suffer from allergies to two groups. They gave the new medication to the subjects in one group and an existing medication to the subjects in the other group. Forty-four percent of those in the treatment group and 28% of those in the control group reported a significant reduction in their allergy symptoms without any drowsiness. Which of the following best describes the inferences the researchers can make based in his results?
They can make inferences about cause and effect, but not about the populations from which the samples were selected.
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 following 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.
A statistics teacher asks the 29 students in his statistics class how many minutes they spent on one homework assignment. The distribution of the variable "time on homework" is
a description of what values the variable takes and how often it takes them.
You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. By the deadline, 1347 teachers return the questionnaire.
all American school teachers.
A simple random sample is
any sample that is selected without replacement. a sample that gives every possible sample of the same size from the same population the same chance to be selected.
A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands) for this year. 28 31 34 35 37 41 42 42 42 47 49 51 52 60 61 67 72 75 77 Suppose each employee in the company receives a $3,000 raise for the next year. The standard deviation of the salaries for the employees will
be unchanged
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 at random, and measures the diameter of every Sugar Maple in each one. This is an example of a
cluster sample
The reason that blocking (as in a randomized block design) is sometimes used in experimentation is to
compensate for anticipated differences in the response variable for different values of a specified "blocking" variable.
Does caffeine improve exam performance? Suppose all students in the 8:30 section of a course are given a "treatment" (two cups of coffee and all students in the 9:30 section are not permitted to have any caffeine before a mid-term exam. Unfortunately, any systematic difference between the two sections on the exam might be due to the fact that the 8:30 and 9:30 classes have different instructors. This is an example of
confounding
The following scatter plot present data on wine consumption (in liters per person per year) and the death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed western countries.
countries that drink more wine have lower death rates from heart disease.
Does caffeine improve exam performance? Suppose all students in the 8:30 section of a course are given a "treatment" (two cups of coffee and all students in the 9:30 section are not permitted to have any caffeine before a mid-term exam. The response variable in this study is
exam performance
Consider the following scatterplot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees celsius) for a certain 2,000-pound car traveling 40 mph
is approximately 0.6
A recent survey by a Canadian magazine on the contribution of universities to the economy was circulated to 394 people who the magazine decided "are the most likely to know how important universities are to the Canadian economy." Which of the following is the main problem with using these results to draw conclusions about the general public's perception?
lack of random selection
An ecologist who is studying starfish population of the species Pisaster. He was interested in the distribution of sizes of this species of starfish. One measure of size is "arm length". Below is a cumulative relative frequency graph for the arm length. Below is a cumulative relative frequency graph for the arm length, in centimeters, of 102 Pisaster individuals.
median = 13 interquartile range = 4
The time it takes a pendulum to complete one back-and-forth swing (its period) is related to its length by the model period=a sq rt length = a(length) ^1/2. An engineer collected data on the period of the pendulum (in seconds) for various lengths in feet for a random sample of the pendulums. The scatterplot of (length) ^1/2 and period is roughly linear
period = 2.047 + 0.0511 (length) ^1/2
A study was conducted to quantify the relationship between stopping distance in feet and air temperature in degrees Celcius for a certain 2,000-pound car traveling 40 mph. If the stopping distance were measured in meters rather than feet, how would the correlation r change?
r would not change, because the calculation of r does not depend on the units used
The histogram below shows the distribution of heights for 100 randomly selected school children in Great Britain.
roughly symmetric, centered at about 150, range: 80
A public opinion poll in Ohio wants to determine if registered voters in the state approve of a measure to ban smoking in all public areas. They select a simple random sample of fifty registered voters from each county in the state and ask whether they approve or disapprove of the measure. This is an example of
stratified random sample.
In comparative trials in medicine, the placebo effect and subconscious bias on the part of the physicians evaluating treatment outcomes can be avoided by using
the double-blind technique.
you have data for many families on the parents' income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school longer. When you make a scatterplot,
the explanatory variable is parent's income and you expect to see a positive association
the correlation coefficient measures
the strength of the linear relationship between two quantitative variables
A study of child development measures the age (in months) at which a child begins to talk and the child's score on an ability test given several years later. The study asks whether the age at which a child talks helps predict the later test score. The least-squares regression line useful for predicting test score from the age is y = 110 - 1.3x. According to this regression line, what happens (on the average) to children who talk one month later than other children.
their predicted test score goes down 1.3 points
a study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is.
yield of the crop