Question 1
Suppose you have an extremely unfair coin: the probability of a head is 1/3 and the probability of a tail is 2/3. If you toss the coin 72 times, how many heads do you expect to see?
A. 12
B. 22
C. 24
D. 26
Question 2
A study of 600 college students taking Statistics 101 revealed that 54 students received the grade of A. Typically 10% of the class gets an A. The difference between this group of students and the expected value is not significant at the 0.05 level. What does this mean in this case?
A. The probability that the difference occurred due to chance is less than 0.05.
B. The probability of getting an A is 10% and only 9% got an A in this study. The difference is less than 5% so it is not significant.
C. There is not enough information to make any conclusion.
D. The probability that the difference occurred due to chance is more than 0.05.
Question 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.
Question 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
Question 5
Suppose you have an extremely unfair coin: the probability of a head is 1/5, and the probability of a tail is 4/5. If you toss the coin 40 times, how many heads do you expect to see?
A. 8
B. 6
C. 5
D. 4
Question 6
On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?
A. 1/5
B. 1/6
C. 1/4
D. 2/5
Question 7
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.
Question 8
A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.)
A. 0.6
B. 0.4
C. 0.7
D. 0.8
Question 9
Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $500. What is your expected value?
A. $0.00
B. -$0.40
C. -$1.00
D. -$0.50
Question 10
Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 5 or a 2, nothing otherwise. What is your expected value?
A. $1.00
B. $0.00
C. $3.00
D. -$1.00
Question 11
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.
Question 12
Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.413. Find the probability that in a given year it will not snow on January 1st in that town.
A. 0.345
B. 0.425
C. 0.587
D. 0.592
Question 13
Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks.
A. The Monday series is closer because 1/6 is closer to 1/2 than is 1/8.
B. The Monday series is closer because 6/12 is closer to 0.5 than is 8/18.
C. The Tuesday series is closer because the 13/18 is closer to 0.5 than is 9/12.
D. The series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series.
Question 14
Of 1308 people who came into a blood bank to give blood, 314 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure (to 3 decimal places).
A. 0.250
B. 0.490
C. 0.240
D. 0.160
Question 15
If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head?
A. 4/9
B. 5/6
C. 7/8
D. 5/8
Question 16
A die with 12 sides is rolled. What is the probability of rolling a number less than 11? Is this the same as rolling a total less than 11 with two six-sided dice? Explain.
A. 2/6
B. 3/6
C. 4/6
D. 5/6
Question 17
Sammy and Sally each carry a bag containing a banana, a chocolate bar, and a licorice stick. Simultaneously, they take out a single food item and consume it. The possible pairs of food items that Sally and Sammy consumed are as follows.
chocolate bar - chocolate bar
licorice stick - chocolate bar
banana - banana
chocolate bar - licorice stick
licorice stick - licorice stick
chocolate bar - banana
banana - licorice stick
licorice stick - banana
banana - chocolate bar
Find the probability that no chocolate bar was eaten.
A. 4/9
B. 5/9
C. 7/9
D. 5/8
Question 18
The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000.
112,000 126,000 90,000 133,000 94,000 112,000 98,000 82,000 147,000 182,000 86,000 105,000
140,000 94,000 126,000 119,000 98,000 154,000 78,000 119,000
A. 0.4
B. 0.6
C. 0.66
D. 0.7
Question 19
If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?
A. 1/8
B. 3/8
C. 5/8
D. 6/8
Question 20
If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. There are 365 days in a year. Express your answer as a fraction.
A. 335/365
B. 334/365
C. 336/365
D. 30/365
Question 21
A random sample of 30 households was selected from a particular neighborhood. The number of cars for each household is shown below. Estimate the mean number of cars per household for the population of households in this neighborhood. Give the 95% confidence interval.
A. 1.14 to 1.88
B. 1.12 to 1.88
C. 1.12 to 1.98
D. 1.14 to 1.98
Question 22
Write possible coordinates for the single outlier such that it would no longer be an outlier.
A. (23, 18)
B. (20, 5)
C. (15, 15)
D. (12, 15)
Question 23
Which graph has two groups of data, correlations within each group, but no correlation among all the data?
Question 24
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
Question 25
The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Determine the amount of variation in the number of cars not explained by the variation time after school.
A. 55%
B. 70%
C. 30%
D. 45%
Question 26
A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error E = 0.01with a 95% degree of confidence.
A. 7,000
B. 8,000
C. 9,000
D. 10,000
Question 27
The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Use the line of best fit to predict the number of cars at time 4 after the end of classes.
A. 7.0
B. 6.0
C. 8.0
D. 3.5
Question 28
A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.
A. 28.0 to 30.0
B. 25.0 to 27.0
C. 29.0 to 31.0
D. 27.0 to 29.0
Question 29
Suggest the cause of the correlation among the data.
The graph shows strength of coffee (y) and number of scoops used to make 10 cups of coffee (x). Identify the probable cause of the correlation.
A.The variation in the x variable is a direct cause of the variation in the y variable.
B. There is no correlation between the variables.
C. The correlation is due to a common underlying cause.
D. The correlation between the variables is coincidental.
Question 30
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
Question 31
Among a random sample of 150 employees of a particular company, the mean commute distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be less than 29.6 miles?
A. 0.8849
B. 0.5
C. 0.1131
D. 0.1151
Question 32
Select the best fit line on the scatter diagram below.
A. A
B. B
C. C
D. All of the lines are equally good
Question 33
Select the best fit line on the scatter diagram below.
A. A
B. B
C. C
D. None of the lines is the line of best fit
Question 34
A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 490 college students showed that 33% of them had, or intended to, cheat on examinations. Find the margin of error for the 95% confidence interval.
A. 0.0432
B. 0.0434
C. 0.0425
D. 0.0427
Question 35
The scatter plot and best-fit line show the relation between the price per item (y) and the availability of that item (x) in arbitrary units. The correlation coefficient is -0.95. Determine the amount of variation in pricing explained by the variation in availability.
A. 5%
B. 10%
C. 95%
D. 90%
Question 36
Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.
A. -0.9
B. 0.9
C. 0.5
D. -0.5
Question 37
Monthly incomes of employees at a particular company have a mean of $5954. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $5747. How many standard deviations is the sample mean from the mean of the sampling distribution?
A. 0.8 standard deviations above the mean
B. 0.8 standard deviations below the mean
C. 7.3 standard deviations below the mean
D. 207 standard deviations below the mean
Question 38
Of the 6796 students in one school district, 1537 cannot read up to grade level. Among a sample of 812 of the students from this school district, 211 cannot read up to grade level. Find the sample proportion of students who cannot read up to grade level.
A. 0.14
B. 0.26
C. 211
D. 0.23
Question 39
The scatter plot and best-fit line show the relation among the data for the price of a stock (y) and employment (x) in arbitrary units. The correlation coefficient is 0.8. Predict the stock price for an employment value of 6.
A. 8.8
B. 6.2
C. 8.2
D. None of the values are correct
Question 40
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)