AP Midyear Review Part 1

A market research company wishes to find out whether the population of students at a university prefers brand A or brand B of instant coffee. A random sample of students is selected, and each student is asked first to try brand A and then to try brand B, or vice versa (with the order determined at random). They then indicate which brand they prefer. This is an example of

• an experiment.

• an observational study, not an experiment.

• stratified sampling design.

• a block design.

• a systematic sampling design.

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CCSS.HSS.IC.B.3

In order to take a sample of 90 members of a local gym, I first divide the members into men and women, and then take a simple random sample of 45 men and a separate simple random sample of 45 women. This is an example of a

• two-step sample

• stratified random sample

• double-blind simple random sample.

• randomized comparative experiment.

• block design.

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CCSS.HSS.IC.B.3

A simple random sample of 1200 adult Americans is selected, and each person is asked the following question:

In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?

Only 39% of those responding answered yes. This survey

• is reasonably accurate since it used a large, simple random sample.

• needs to be larger since only about 24 people were drawn from each state.

• probably understates the percentage of people that favor a system of national health insurance.

• is very inaccurate, but neither understates nor overstates the percentage of people that favor a system of national health insurance. Since simple random sampling was used, it is unbiased.

• probably overstates the percentage of people that favor a system of national health insurance.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

A study of the effects of running on personality involved 231 male runners who each ran about 20 miles a week. The runners were given the Cattell Sixteen Personality Factors Questionnaire, a 187-item multiple-choice test often used by psychologists. A news report (New York Times, Feb. 15, 1988) stated, “The researchers found statistically significant personality differences between the runners and the 30-year-old male population as a whole.” A headline on the article said, “Research has shown that running can alter one’s moods.” Which of the following statements is true?

• The study was not a designed experiment.

• This study was an experiment, but not a double-blind experiment.

• This study was a blocked experiment.

• This study was a randomized, double-blind experiment.

• The study was a double-blind experiment, but not a randomized experiment.

Tags

CCSS.HSS.IC.B.3

A researcher wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the children’s age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities.

r = 0.9 x(bar)= 6.5 y(bar)= 6.6 s_X = 3.6 s_Y = 1.2

The slope of the least-squares line is

• 0.30

• 0.88

• 1.01

• 2.7

• 3.0

Tags

CCSS.HSS.ID.C.8

A least-squares regression line is fitted to a set of data. If one of the data points has a positive residual, then

• the correlation between the values of the response and explanatory variables must be positive.

• the point must lie above the least-squares regression line.

• the slope of the LSRL must be positive.

• the point must lie near the right edge of the scatter plot.

• all of the above.

Tags

CCSS.HSS.ID.B.6B

The correlation coefficient is:

• 92.7%

• 0.963

• 0.927

• 3.3684

• 1.835

Using the above data, is there strong evidence (and if so, why) of a straight-line relationship between sales and profits?

• Yes, because the slope of the least-squares line is positive.

• No, because the correlation coefficient is positive.

• Yes, the correlation coefficient and coefficient of determination are close to 1.

• It is impossible to say because we are not given the actual value of the correlation.

• None of the above.

What is the correlation between selling price and appraised value?

• 0.1126

• 0.861

• 0.928

• 0.851

• 0.922

Tags

CCSS.HSS.ID.C.8

A least squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of many young children. The equation of the line is y(hat)=16.6+0.65t, where y(hat) is the predicted weight and t is the age of the child. A 20-month-old child in this group has an actual weight of 25 pounds. Which of the following is the residual weight, in pounds, for this child?

• -7.85

• -4.60

• 4.60

• 5.00

• 7.85

Tags

CCSS.HSS.ID.B.6B