20 multiple choice questions
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20_statistic_questions.docx
(1) Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. He reshuffled the cards and dealt 30 cards. This time, the number of red cards exceeded the number of black cards by 10. Determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.
A. The first series is closer because 1/10 is farther from 1/2 than is 1/8.
B. The series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.
C. The second series is closer because 20/30 is closer to 1/2 than is 14/20.
D. The first series is closer because the difference between red and black is smaller than the difference in the second series.
(2) In the first series of rolls of a die, the number of odd numbers exceeded the number of even numbers by 5. In the second series of rolls of the same die, the number of odd numbers exceeded the number of even numbers by 11. Determine which series is closer to the 50/50 ratio of odd/even expected of a fairly rolled die.
A. The second series is closer because the difference between odd and even numbers is greater than the difference for the first series.
B. The first series is closer because the difference between odd and even numbers is less than the difference for the second series.
C. Since 1/2 > 1/5 > 1/11, the first series is closer.
D. The series closer to the theoretical 50/50 cannot be determined unless the total number of rolls for both series is given.
(3) A study of students taking Statistics 101 was done. Four hundred students who studied for more than 10 hours averaged a B. Two hundred students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 level. What does this mean?
A. The probability that the difference was due to chance alone is greater than 0.01.
B. There is less than a 0.01 chance that the first group’s grades were better by chance alone.
C. The improvement was due to the fact that more people studied.
D. There is not enough information to make any conclusion.
(4) The distribution of B.A. degrees conferred by a local college is listed below, by major.
Major Frequency
English 2073
Mathematics 2164
Chemistry 318
Physics 856
Liberal Arts 1358
Business 1676
Engineering 868
9313
What is the probability that a randomly selected degree is not in Business?
A. 0.7800
B. 0.8200
C. 0.8300
D. 0.9200
(5) A researcher wishes to estimate the mean amount of money spent per month on food by households in a certain neighborhood. She desires a margin of error of $30. Past studies suggest that a population standard deviation of $248 is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.
A. 274
B. 284
C. 264
D. 272
(6) Among a random sample of 500 college students, the mean number of hours worked per week at non-college related jobs is 14.6. This mean lies 0.4 standard deviations below the mean of the sampling distribution. If a second sample of 500 students is selected, what is the probability that for the second sample, the mean number of hours worked will be less than 14.6?
A. 0.5
B. 0.6179
C. 0.6554
D. 0.3446
(7) A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 27% of them had, or intended to, cheat on examinations. Find the 95% confidence interval.
A. 0.2323 to 0.3075
B. 0.2325 to 0.3075
C. 0.2325 to 0.3185
D. 0.2323 to 0.3185
(8) Which point below would be an outlier if it were on the following graph?
A. (25, 20)
B. (5, 12)
C. (7, 5)
D. (5, 3)
(9) A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.
A. Conclusion: Support the claim that the mean is equal to 16 ounces.
B. Conclusion: Support the claim that the mean is greater than 16 ounces.
C. Conclusion: Support the claim that the mean is not equal to 16 ounces.
D. Conclusion: Support the claim that the mean is less than 16 ounces.
(10) A study of a brand of “in the shell peanuts” gives the following results:
A significant event at the 0.01 level is a fan getting a bag with how many peanuts?
A. 30 peanuts
B. 25 or 30 peanuts
C. 25 or 55 peanuts
D. 25 peanuts
(11) A two-tailed test is conducted at the 5% significance level. Which of the z-scores below is the smallest one that leads to rejection of the null hypothesis?
A. 1.12
B. 1.48
C. 1.84
D. 2. 15
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(12) The principal of a middle school claims that annual incomes of the families of the seventh-graders at his school vary more than the annual incomes of the families of the seventh-graders at a neighboring school, which have variation described by = $13,700. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply. A. The current seventh graders at the principal’s school B. Seventh graders’ families at the school with a standard deviation of $13,700 C. All of the families of the class of seventh graders at the principal’s school D. All seventh graders’ families |
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(13) The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.
A. All games played by the team in question in which the attendance is over 4000
B. All future home games to be played by the team in question
C. All home games played by the team in question
D. None of the populations given are appropriate
(14) The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 18 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3? Explain your answer.
A. Smaller. E decreases as the square root of the sample size gets larger.
B. Smaller. E increases as the square root of the sample size gets larger.
C. Larger. E decreases as the square root of the sample size gets larger.
D. Larger. E increases as the square root of the sample size gets larger.
(15) The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 25 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3?
A. Smaller. E increases as the square root of the sample size gets larger.
B. Smaller. E decreases as the square root of the sample size gets larger.
C. Larger. E decreases as the square root of the sample size gets larger.
D. Larger. E increases as the square root of the sample size gets larger.
(16) A large test statistic F tells us that the sample means __________ the data within the individual samples, which would be unlikely if the population’s means really were equal (as the null hypothesis claims).
A. differ more than
B. differ less than
C. are equal to
D. do not vary with
(17) One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
|
|
Colorblind |
Not Colorblind |
Total |
|
Male |
8 |
52 |
60 |
|
Female |
2 |
38 |
40 |
|
Total |
10 |
90 |
100 |
Find the value of the χ2 statistic for the data above.
A. 1.463
B. 1.852
C. 1.947
D. 1.949
(18) One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
|
|
Colorblind |
Not Colorblind |
Total |
|
Male |
8 |
52 |
60 |
|
Female |
2 |
38 |
40 |
|
Total |
10 |
90 |
100 |
If gender and colorblindness are independent, find the expected values corresponding to the four combinations of gender and colorblindness, and enter them in the following table along with row and column totals.
|
|
Colorblind |
Not Colorblind |
Total |
|
Male |
|
|
|
|
Female |
|
|
|
|
Total |
|
|
|
A. Male Colorblind 6.0; Male Not Colorblind 54.0
B. Male Colorblind 7.0; Male Not Colorblind 53.0
C. Male Colorblind 8.0; Male Not Colorblind 52.0
D. Male Colorblind 6.0; Male Not Colorblind 53.0
(19) One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
|
|
Colorblind |
Not Colorblind |
Total |
|
Male |
7 |
53 |
60 |
|
Female |
1 |
39 |
40 |
|
Total |
8 |
92 |
100 |
Find the value of the χ2 statistic for the data above.
A. 1.325
B. 1.318
C. 1.286
D. 1.264
|
|
Colorblind |
Not Colorblind |
Total |
|
Male |
8 |
52 |
60 |
|
Female |
2 |
38 |
40 |
|
Total |
10 |
90 |
100 |
State the null and alternative hypothesis for the test associated with this data.
A.
H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are not related in any way.
B.
H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are related in some way.
C.
H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are not related in any way.
D.
H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are related in some way
