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Data Analysis
Experimental Design
Free Response
Inference
Probability
100
Suppose the correlation between two variables is r = .28. What will the new correlation be if .17 is added to all values of the x-variable, every value of the y variable is doubled, and the two variables are interchanged? (A) .28 (B) .45 (C) .56 (D) .90
(A) .28 Explanation: The correlation is not changed by adding the same number to every value of one of the variables, by multiplying every value of one of the variables by the same positive number, or by interchanging the x- and y- variables.
100
A company wishes to survey what people think about a new product it plans to market. They decide to randomly sample from their customer database as this includes phone numbers and addresses. This procedure is an example of which type of sampling?
Convenience Samples. They are based on on choosing individuals who are easy to reach. Data obtained from convenience samples tend to be highly unrepresentative of the entire population.
100
Does cell phone radiation increase a person's risk of getting cancer? How can an observational study be performed?
Interview a random sample of people as to whether or not they use a cell phone and whether or not they have cancer. Compare the proportion of cell phone users who have cancer to the proportion of non-cell phone users who have cancer.
100
Which of the following is the proper use of a cji-square test of independence? a) To test whether the distribution of counts on a categorical variable matches a claimed distribution b) To test whether the distribution of counts on a numerical variable matches a claimed distribution c) To test whether the distribution of two differetn groups on the same categorical variable matches d) To test whether two categorical variables on the same subjects are related e) To test whether two numerical variables on the same subjects are related
d) Chi-square tests are for categorical data
100
According to one poll, only 8 percent of the public say they "trust congress." In a simple random sample of ten people, what is the probability that at least one person "trusts congress"? (A) .188 (B) .378 (C) .434 (D) .566
(D) .566 Explanation: P(at least one) = - P(none) = 1 - (.92)^10 = 1- .434 = .566
200
If ten executives have salaries of $80,000, six have salaries of $75,000, and three have salaries of $70,000, what is the median salary?
$80,000. Explanation: The median is the middle score when they are arranged in ascending or descending order. Noe there are a total of 19 scores.
200
What is bias in conducting surveys?
A tendency to favor the selection of certain members of a population.
200
During the 2006 NFL postseason play, the 12 participating teams scored the following numbers of passing touchdowns: {0,0,1,1,1,2,2,3,3,3,3,5} The trimean is defined as, Q1+ 2Med + Q3/4. Compute the trimean for the aboved data.
1+2(2)+3/4= 2.
200
For a given large sample size, which of the following gives the smallest margin of error in calculating a confidence interval for a population proportion? a.) 90% confidence with PredictedP=.15 b.) 95% confidence with PredictedP=.15 c.) 99% confidence with PredictedP=.15 d.) 90% confidence with PredictedP=.23 e.) 95% confidence with PredictedP=.23
A) Lower levels of confidence lead to narrower confidence intervals.
200
A mortgage company advertises that 85 percent of applications are approved. In a random sample of 30 applications, what is the expected number that will be turned down? (A) 30(.85) (B) 30(.15) (C) 85(.70) (D) 85(.30)
(B) Explanation: The probability of an application being turned down is 1-.85=.15, and the expected value of a binomial with n=30 and p=.15 is np=30(.15).
300
If every man married a woman who was exactly 3 years younger than he, what would be the correlation between the ages of married men and women?
1. Explanation: On the scatterplot, all the points would lie perfectly on a straight line sloping up to the right, so r=1.
300
A telephone survey with regard to support of a bond issue resulted in: Age 21-30 31-40 41-50 51-60 For 45 32 28 25 Against 30 43 47 50 Which sampling strategy was most likely used?
Stratified sampling. In stratified sampling, the population is divided into homogeneous groups called strata, and random samples of persons from all strata are chosen.
300
Suppose we calculate the melting points of eight metal rods and find the mean to be 1,400 degrees Fahrenheit with a standard deviation of 90 degrees Fahrenheit. What would be the mean and standard deviation of the melting points of the eight rods if the eight measurements were converted to Celsius?
The new mean is 760 degrees Celsius and the new standard deviation is 50 degrees Celsius. The size of the sample, n=8, is extraneous information.
300
A telephone survey of 400 registered voter showed that 256 had not yet made up their minds 1 month before the election. At what confidence level can we say that between 60 percent and 68 percent of the electorate were still undecided at that time? a) 2.4% b.) 64% c.) 90.4% d.) 95.3% e.) 96.7%
c.) 90.4
300
The diastolic pressure among 20 to 30 year olds is roughly normal. If 10 percent have levels above 86 mmHg, and 20 percent have levels below 69 mmHg, what is the mean of this distribution? (A) 74.7 mmHg (B) 75.7 mmHg (C) 77.5 mmHg (D) The mean cannot be calculated from the given information.
(B) 75.7 Explanation: Solving the system of equations (mean + 1.282*Standard Deviation = 86, mean - .842*Standard Deviation = 69) gives mean = 75.7
400
Consider the three points (4,33), (5,27), and (6,15). Given any straight line, we can calculate the sum of the squares of the three vertical distances from these points to the line. What is the smallest possible value this sum can be?
6. Explanation: Using your calculator, find the regression line to be y hat=70-9x. The regression line minimizes the sum of the squares of the vertical distances between the points and the line. In this case, (4,34), (5,25), and (6,16) are on line and so the minimum sum is (33-34)^2+(27-25)^2+(15-16)^2=6.
400
A television network conducts a weekly survey to determine the proportion of viewers who watch various programs. For the coming year, they decide to double the sample size. The main benefit of this is....?
Decrease the standard deviation of the sampling distribution.
400
Suppose a police breathalyzer unit will correctly test positive for 98 percent of legally drunk drivers, but will also give a false positive reading for 3 percent of drivers whose actual blood alcohol concentration is under the limit. If 5 percent of late Saturday night drivers are legally drunk, and an officer arrests two drivers with positive readings, what is the probability that exactly one of the two is guilty of driving drunk?
P(drunk-pos test)=.049 P(sober-pos test)= .0285 P (pos test) = .0775 P(drunk|pos test)= .6323 P(sober| pos test)= .3677 P(exactly 1 success in 2 trials)= .4650
400
What is the probability of a Type 2 error when a hypothesis test is being conducted at the 5 percent significance level? (A) .05 (B) .10 (C) There is insufficient information to answer this question
(C) There is insufficient information to answer this question
400
The average noise level in a bar is 36 decibels with a standard deviation of 5 decibels. Assuming a normal distribution, what is the probability the noise level is between 30 and 40 decibels? (A) .327 (B) .337 (C) .381 (D) .673
(D) .673 Explanation: On the TI-84, normalcdf (30, 40, 36, 5) = .673
500
Using the most commonly accepted definition of outliers, a set has five outliers. If every value of the set is increased by 20 percent, how many outliers will there now be?
Five. Explanation: Increasing every value by 20 percent will also increase Q1, Q3, and the IQR as well as both Q1-1.5(IQR) and Q3+1.5(IQR) by the same 20 percent.
500
A critical difference between experiments and observational studies is...?
An experiment often suggests a casual relationship, whereas an observational study only suggest an association. Observational studies can not be used to show direct cause-and-effect relationships as experiments can.
500
Does cell phone radiation increase a person's risk of getting cancer? Describe, using this topic, how an experiment can be performed.
From a group of non-cancer volunteers, use chance to pick half half to use cell phones for some period of years while the remaining half are instructed to restrain from using cell phones for the same period of time. At the end of the time period, compare the proportion of people in each group who came down with cancer.
500
In a one-sided hypothesis test for the mean, for a random sample of size 15 the t-score of the sample mean is 2.615. Is this significant at the 5 percent level? At the 1 percent level? (A) Significant at the 1 percent but not at the 5 percent level (B) Significant at the 5 percent level but not at the 1 percent level (C) Cannot be determined from the given information
(B) Significant at the 5 percent level but not at the 1 percent level
500
Suppose 56 percent of eight to twelve year olds expect to have "a great life." In an SRS of 125 eight to twelve year olds, what is the probability that between 50 percent and 60 percent will say they expect to have a "a great life?" a.) .2721 b.).5402 c.).6723 d.).7279 e.).8640
D).7279