AP Exam Prep 2

Suppose the probability that a softball player gets a hit in any single at-bat is 0.300. Assuming that her chance of getting a hit on a particular time at bat is independent of her other times at bat, what is the probability that she will not get a hit until her fourth time at bat in a game?

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The probability that Color Me Dandy wins a horse race at Batavia Downs given good track conditions is 0.60. The probability of good track conditions on any given day is 0.85. What is the probability that Color Me Dandy wins or the track conditions are good?

• 0.94

• 0.51

• 0.49

• 0.06

• The answer can not be determined from the info provided

Sports Illustrated planned to ask a random sample of Division I college athletes, “Do you believe performance-enhancing drugs are a problem in college sports?” How many athletes must be interviewed to estimate the proportion concerned about use of drugs within ±2% with 90% confidence?

• 17

• 21

• 1680

• 1702

• 2401

The distribution of grade point averages for a certain college is approximately Normal with a mean of 2.5 and a standard deviation of 0.6. Within which of the following intervals would we expect to find approximately 81.5% of all GPAs for students at this college?

• (0.7, 3.1)

• (1.3, 3.7)

• (1.9, 3.7)

• (1.9, 4.3)

• (0.7, 4.3)

Which of the following will increase the power of a significance test?

• Increase the Type II error probability.

• Decrease the sample size.

• Reject the null hypothesis only if the P-value is smaller than the level of significance.

• Increase the significance level α.

• Select a value for the alternative hypothesis closer to the value of the null hypothesis.

A certain candy has different wrappers for various holidays. During Holiday 1, the candy wrappers are 30% silver, 30% red, and 40% pink. During Holiday 2, the wrappers are 50% silver and 50% blue. Forty pieces of candy are randomly selected from the Holiday 1 distribution, and 40 pieces are randomly selected from the Holiday 2 distribution. What are the expected value and standard deviation of the total number of silver wrappers?

• 32, 18.4

• 32, 6.06

• 32, 4.29

• 80, 18.4

• 80, 4.29

A random sample of 200 New York State voters included 88 Republicans, while a random sample of 300 California voters produced 141 Republicans. Which of the following represents the 95% confidence interval that should be used to estimate the true difference in the proportions of Republicans in New York State and California?

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Inference about the slope β of a least-squares regression line is based on which of the following distributions?

• The t distribution with n − 1 degrees of freedom

• The standard Normal distribution

• The chi-square distribution with n − 1 degrees of freedom

• The t distribution with n − 2 degrees of freedom

• The Normal distribution with mean μ and standard deviation σ

The correlation between the heights of fathers and the heights of their (grownup) sons is r = 0.52, both measured in inches. If fathers’ heights were measured in feet instead, the correlation between heights of fathers and heights of sons would be

• much smaller than 0.52.

• slightly smaller than 0.52.

• unchanged; equal to 0.52.

• slightly larger than 0.52.

• much larger than 0.52.

An agricultural station is testing the yields for six different varieties of seed corn. The station has four large fields available, which are located in four distinctly different parts of the county. The agricultural researchers consider the climatic and soil conditions in the four parts of the county as being unequal but are reasonably confident that the conditions within each field are fairly similar throughout. The researchers divide each field into six sections and then randomly assign one variety of corn seed to each section in that field. This procedure is done for each field. At the end of the growing season, the corn will be harvested, and the yield, measured in tons per acre, will be compared. Which one of the following statements about the design is correct?

• This is an observational study because the researchers are watching the corn grow.

• This a randomized block design with fields as blocks and seed types as treatments.

• This is a randomized block design with seed types as blocks and fields as treatments.

• This is a completely randomized design because the six seed types were randomly assigned to the four fields.

• This is a completely randomized design with 24 treatments—6 seed types and 4 fields.