# Statistics practice problems 2016

March 14, 2016

Question
1. When collecting water data from different sample locations in a lake, a researcher uses the ” line transect method” by stretching a single rope with containers tied to it across the lake and collects samples at every interval of 5 meters. Indetify which type of sampling is used here.

A. Random Sampling
B. Convenience Sampling
C. Cluster sampling
D. Systematic sampling

2. Researchers from the National Institutes of Health want to determine the current rate of smoking among adults in New York. They conduct a survey of 500 adults of each gender in New York. Identify the types of study for this description.

A. Observational and Prospective
B. Observational and Cross-sectional
C. Experimental and Retrospective
D. Experimental and Cross-sectional

Problems 3 and 4 refer to the following data:
These data show the daily gross amounts (in millions of dollars) earned in box office receipts (first 2 weeks) of the movie “Ghost”.
40 22 27 29 10 10 8
20 24 14 11 9 4 4

3. Find the mean and median to the nearest tenth for this sample data.

A. Mean = 22.0, Median = 12.5 B. Mean = 16.6, Median = 12.5
C. Mean = 22.0, Median = 11.0 D. Mean = 16.6, Median = 11.0

4. Which of the following gives the sample standard deviation and the range of the data?

A. SD = 10.7, Range = 18
B. SD = 10.7, Range = 36
C. SD = 12.5, Range = 18
D. SD = 12.5, Range = 36

5. The following frequency distribution summarized ACT Math scores of 50 randomly chosen college students. Estimate their mean ACT Math score by using class midpoints for the ACT scores.

ACT Score Frequency
A. Mean = 19.58 1 – 6 3
B. Mean = 18.62 7 – 12 6
C. Mean = 18.00 13 – 18 12
D. Mean = 21.57 19 – 24 16
25 – 30 9
31 – 36 4
6. Which one of the following describes a quantitative, discrete variable?

A. Letter grade of students in a class (A, B, C, D, and U).
B. Mean IQ Score of students in a class.
C. Height of student in a class.
D. Number of students in a class.

Problems 7 and 8 refer to the following histogram, which represents the ages of people randomly selected from those who entered Bucs High School during last Friday morning (Parent-teacher meeting):

7. What percent of people with ages less than 50 entered the school?

A. 45.8% B. 60.4% C. 54.2% D. 57.6%

8. Within which age group would the first quartile (Q1) fall?

A. 10?19 B. 20?29 C. 30?39 D. 70?79

Problems 9 and 10 refer to the following box-and-whisker plots to compare homework time per night with TV time per night for the same group of sophomores.

Homework time (in minutes)

TV time (in minutes)

9. Which distribution shape most likely describes the boxplot homework time?

A. Skewed right
B. Skewed left
C. Uniform
D. Normal

10. Which of the following statements is false concerning the box-and-whisker plots?

A. TV time has a larger interquartile range (IQR) than Homework time
B. TV time has a larger median than Homework time
C. TV time has a larger maximum than Homework time
D. TV time has a larger Q1 than Homework time

11. Out of fifty randomly chosen adults age 65 or older, at least 15 had a Facebook account. What is the complement of this description?

12. If P(A) = 0.08, which one of the following statements is true?

A. The probability of the complement of event A is 0.32.
B. The probability of event A happening twice in a row (with replacement) is 0.0064.
C. Event A is an “unusual” event
D. For each 8 times event A happens, there are 100 times in which A doesn’t happen.

Problems 13 and 14 refer to the following table:

The following table is the probability distribution for the number in a group of five randomly selected males who have a form of color blindness. The probabilities are based on data from the National Institutes of Health. In the table, x = the number of males who have a form of color blindness, and P(x) is the probability of x males having a form of color blindness.

x 0 1 2 3 4 5
P(x) 0.658 0.287 0.05 0.004 0.001 0+

13. Determine the probability that at least one of the males has a form of colorblindness.

A. 0.658
B. 0.342
C. 0.945
D. 0.055

14. Determine the expected number (mean) of males who have a form of color blindness.

A. 0.05
B. 0.2
C. 0.4
D. 3

15. A bag contains 6 red marbles, 4 blue marbles, and 3 green marbles. If you draw two marbles, without replacement, what is the probability that you get 2 red marbles?

A. 0.1775 B. 0.1923 C. 0.8782 D. 0.8462

16. A widely accepted fact is that 80% of all people have brown eyes. What is the probability of randomly selecting 2 people and neither of them has brown eyes?

A. 1.6 B. 0.04 C. 0.64 D. 0.16

17. According to one study, 19% of all third graders have their own cell phone. Six third graders are randomly chosen. What is the probability that less than 2 of them have a cell phone? (NOTE: this problem meets all the requirements of a binomial situation.)

A. 0.23 B. 0.4 C. 0.68 D. 0.91

Problems 18 through 24 refer to the following:
Daily temperatures in Honolulu are normally distributed with a mean of 73 degrees and a standard deviation of 5 degrees.

18. What is the z-score that corresponds to a temperature of 80 degrees within this distribution?

A. ?1.4 B. 1.4 C. 0.85 D. 1.03

19. What symmetric interval about the mean will contain approximately 99.7% of the daily temperatures?

A. 58 to 88 B. 63 to 83 C. 68 to 78 D. 53 to 93

20. What is the probability that a randomly selected day will have a temperature below 65 degrees?

A. 0.95 B. ?1.6 C. 1.6 D. 0.05

21. What temperature is at the 40th percentile (rounded to the nearest whole number)?

A. 72 B. 74 C. 69 D. 29

22. What percentage of daily temperatures are between 75 degrees and 80 degrees?

A. 0.34 B. 0.26 C. 0.84 D. 0.08

23. Suppose random samples of 25 daily temperatures are selected repeatedly from the population. What is the mean and standard deviation for the sampling distribution of sample means?

A. Mean = 73, SD = 10 B. Mean = 73, SD = 25
C. Mean = 73, SD = 5 D. Mean = 73, SD = 1

24. What is the probability that a sample of 25 daily temperatures chosen at random have an average above 75 degrees?

A. 0.9773 B. 0.3446 C. 0.0228 D. 0.6554

Problems 25 through 27 are based on the information provided directly below:
Suppose you want to determine the average GPA of all ASU students. You randomly select 33 students and find that those students had a mean GPA of 2.68.

25. Compute a 99% confidence interval for the mean GPA of all ASU students, if the sample standard deviation was s = 0.9.

A. 2.68 ± 0.372
B. 2.68 ± 0.429
C. 2.68 ± 0.404
D. 2.68 ± 0.451

26. Assume the population standard deviation is estimated to be ? = 0.8. What sample size, n, is needed to obtain a margin of error of 0.25 with 99% confidence?

A. 68
B. 49
C. 30
D. 56

27. Consider the situation given in Problem #26. Which of the following would produce a confidence interval with a larger margin of error?

A. Using a confidence level of 90%
B. Using a smaller estimate for ?
C. Using a smaller sample size
D. All of the above A through C

28. Which of the following statements is false?

A. The Central Limit Theorem states that a sampling distribution of means will not have the same shape as the population distribution from which it is taken.

B. The Central Limit Theorem states that the mean of a sampling distribution of means will have the same mean as the population distribution from which it is taken.

C. The Central Limit Theorem states that the standard deviation of a sampling distribution of means (with n > 1) will have a smaller standard deviation as the population distribution from which it is taken.

D. None of A through C are false.

29. If your population is normally distributed, which of the following statements regarding confidence intervals of population means is always true?

A. When ? is known, we use the critical value, z.
B. When n >30, we use the critical value, z.
C. When n < 30, we use the critical value, t.
D. None of A through C are always true.

30. A researcher is interested in conducting a poll on the President’s approval rating. A margin of error of at most 2% is desired. How many people must be sampled to meet this requirement at the 95% confidence level if no preliminary estimate of p-hat is known?

A. 1691
B. 250
C. 2401
D. 170

31. The marketing director for a cereal company would like to know what proportion of households that received free samples of the cereal with their newspapers later purchase the cereal. A random sample of 250 households showed that 72 purchased the cereal after receiving the free sample. Construct a 95% confidence interval for the proportion of all households that purchased the cereal after receiving the free sample.

A. 0.25 to 0.32
B. 0.23 to 0.34
C. 0.66 to 0.78
D. 0.21 to 0.36

32. The US census reported that it takes workers an average of 28 minutes to drive home from work. City officials in New York believe that it takes workers in their city less than 28 minutes to drive home from work. Which of the following gives the proper alternative hypothesis to test the claim that the average length of time for workers in New York to drive home from work is under 28 minutes?

A. H1: µ = 28
B. H1: µ < 28
C. H1: µ > 28
D. H1: µ ? 28

33. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 such bears has a mean weight of 182.9 lb. Assuming that ? is known to be 121.8 lb, use a 0.05 significance level to test the claim that the population mean of all such bear weights is greater than 150 lb. Compute the test statistic for this test with H1: ? > 150.

A. ?1.98
B. 2.73
C. 1.98
D. ?2.73

34. The Pew Research Center conducted a survey of 1007 randomly selected adults and found that 791 of those adults know what Twitter is. Use a 0.01 significance level to test the claim that more than 75% of adults know what Twitter is. Compute the P value for this test.

A. 0.0001
B. 2.76
C. 2.6
D. 0.0046

35. Suppose for a particular hypothesis test, a = 0.05 and the P value = 0.10. Which of the following statements is false?

A. We reject the null hypothesis.
B. We fail to reject the null hyppthesis.
C. The observed result is “not unusual”.
D. The computed test statistic, z, does not fall in the shaded critical region of the tail in the normal curve.

36. A sample of 40 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The average height was 67.9 inches and the average pulse rate was 85.2 bpm. The linear correlation coefficient is r = 0.802 and the equation of the regression line is found to be ? = 18.26 + 0.920x , where x represents height. Find the best predicted pulse rate of a woman who is 70 inches tall.

A. 85.2 bpm
B. 82.6 bpm
C. 54.0 bpm
D. 67.9 bpm

37. A correlation coefficient of ?0.96 between two quantitative variables A and B indicates that

A. As A increases, B tends to increase.
B. Changes in A cause changes in B.
C. As A increases, B tends to decrease.
D. There is a very weak association between A and B, and change in A will not affect B.

38. Of the scatterplot graphs below, which one represents the strongest, positive linear correlation?

A. B.

C. D.

Problems 39 and 40 refer to the following table pairing the values of the Consumer Price Index (CPI) and the national average cost of a slice of pizza:

CPI 30.2 48.3 112.3 162.2 191.9 197.8
Pizza Cost 0.15 0.35 1 1.25 1.75 2

39. Compute the least squares regression line for the cost of pizza.

A. ? = ? 0.1616x ? 0.0101
B. ? = 0.0101x ? 0.1616
C. ? = ? 0.0101x + 0.1616
D. ? = 0.1616x ? 0.0101

40. Calculate the linear correlation coefficient between the two variables.

A. 0.985
B. ?0.985
C. 0.971
D. ?0.971

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