Penn Foster Exam 050272RR PROBABILITY
1. In the binomial probability distribution, p stands for the
A. number of successes.
B. probability of failure in any given trial.
C. probability of success in any given trial.
D. number of trials.
2. Find the z-score that determines that the area to the right of z is 0.8264.
3. The possible values of x in a certain continuous probability distribution consist of the infinite number of values between 1 and 20. Solve for P(x = 4).
4. A continuous probability distribution represents a random variable
A. that has a definite probability for the occurrence of a given integer. B. having outcomes that occur in counting numbers.
C. having an infinite number of outcomes that may assume any number of values within an interval.
D. that’s best described in a histogram.
5. Which of the following is a discrete random variable?
A.The average daily consumption of water in a household
B.The weight of football players in the NFL
C. The number of three-point shots completed in a college basketball game
D. The time required to drive from Dallas to Denver
6. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviation
of 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normal distribution.)
7. The table above gives the probabilities of combinations of religion and political parties in a city in the United States. What is the probability that a randomly selected person will be a Protestant and at the same time be a Democrat or a Republican?
8. An apartment complex has two activating devices in each fire detector. One is smoke-activated and has a probability of .98 of sounding an alarm when it should. The second is a heat-sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector. What is the probability that both activating devices will work properly?
9. For each car entering the drive-through of a fast-food restaurant, x = the number of occupants. In this study, x is a
A. dependent event.
B. continuous quantitative variable. C. joint probability.
D. discrete random variable.
10. Each football game begins with a coin toss in the presence of the captains from the two opposing teams. (The winner of the toss has the choice of goals or of kicking or receiving the first kickoff.) A particular football team is scheduled to play 10 games this season. Let x =the number of coin tosses that the team captain wins during the season. Using the appropriate table in your textbook, solve for P( 4 ≤ x ≤8).
11. What is the value of ?
12. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Given that an animal is brown-haired, what is the probability that it’s short-haired?
13 A new car salesperson knows that she sells a car to one customer out of 20 who enter the showroom. Find the probability that she’ll sell a car to exactly two of the next three customers.
14. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are nonnally distributed. The standard deviation is 3.061. What is the probability that the Burger Bin will sell 12 to 18 burgers in an hour?
15. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Let A be the event “shaggy and brown-haired.” Compute P(Ac).
16 If event A and event B are mutually exclusive, P(A or B) =
A. P(A) + P(B) – P(A and B).
B. P(A +B).
C. P(A) -P(B).
D. P(A) + P(B).
17. The probability of an offender having a speeding ticket is 35%, having a parking ticket is 44%, having both is 12%. What is the probability of an offender having either a speeding ticket or a parking ticket or both?
18. Which of the following is correct concerning the Poisson distribution?
A. The mean is usually larger than the variance.
B. The mean is usually smaller than the variance.
C. The event being studied is restricted to a given span of time, space, or distance.
D: Each event being studied must be statistically dependent on the previous event.
19. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. If hourly sales fall between 24 and 42 burgers 49.85% of the time, the standard deviation is burgers.
20. Assume that an event A contains 10 observations and event B contains 15 observations. If the intersection of events A and B contains exactly 3 observations, how many observations are in the union of these two events?
A. 0 B. 22 C. 10 D. 28
Exam: 050273RR – SAMPLING DISTRIBUTIONS AND ESTIMATION: HYPOTHESIS TESTING
1. Which of the following statements correctly compares the t-statistic to the z-score when creating a confidence interval?
A. The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution.
B. You can use t all the time, but for n ≥ 30 there is no need, because the results are almost identical if you use t or z.
C. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.
D. Use t when the sample size is small, and the resulting confidence interval will be narrower.
2.. A portfolio manager was analyzing the price-earnings ratio for this year’s performance. His boss said that the average price-earnings ratio was 20 for the many stocks that his firm had traded, but the portfolio manager felt that the figure was too high. He randomly selected a sample of 50 price-earnings ratios and found a mean of 18.17 and a standard deviation of 4.60. Assume that the population is normally
distributed, and test at the 0.01 level of significance. Which of the following is the correct decision rule for
the manager to use in this situation?
A. Because 2.81 is greater than 2.33, reject H 0. At the 0.01 level, the sample data suggest that the average price-earnings ratio for the stocks is less than 20.
B: If t > 2.68 or if t < -2.68, reject H0.
C, Because -2.81 falls in the rejection region, reject H0. At the 0.01 level, the sample data suggest that the average price earings ratio for the stocks is less than 20.
D. If z > 2.33, reject H0.
3. To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?
A. 18.3, 95%
c. 20.3, 95%
D. 20.3, 0.95
4. Which of the following statements about hypothesis testing is false?
A. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.
B. The rejection region is always given in units of standard deviations from the mean.
C. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.
D. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.
5. Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that s = $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices?
6. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the test statistic?
7. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While the true value of the population standard deviation is unknown, the researcher is reasonably sure that the population is normally distributed. Given this information, which of the following statements would be correct?
A. The researcher should use the z-test because the population is assumed to be normally distributed.
B. The t-test should be used because the sample size is small.
The t-test should be used because sigma is unknown and the sample size is small.
C. The t-test should be used because a and p. are unknown.
D. The researcher should use the z-test because the sample size is less than 30.
8. When the confidence coefficient is large, which of the following is true?
A. Its value is close to 1.0, but not larger than 1.0.
B. It’s more likely that the test will lead you to reject the null hypothesis. C. Its value is I .0 or larger.
D. The confidence interval is narrow.
9. What sample size is required from a very large population to estimate a population proportion within
0.05 with 95% confidence? Don’t assume any particular value for p.
10. If the level of significance (a) is 0.005 in a two-tail test, how large is the nonrejection region under the curve of the t distribution?
11. A mortgage broker is offering home mortgages at a rate of 9.5%, but the broker is fearful that this value is higher than many others are charging. A sample of 40 mortgages filed in the county courthouse shows an average of 9.25% with a standard deviation of 8.61%. Does this sample indicate a smaller average? Use o.
= 0.05 and assume a normally distributed population.
A. Yes, because the sample mean of9.25 is below 9.5.
B. Yes, because the test statistic is greater than -1.645.
C. No, because the test statistic falls in the acceptance region.
D. No, because the test statistic is -1.85 and falls in the rejection region.
12. In the statement of a null hypothesis, you would likely find which of the following terms?
13Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the p-value you would report for this test?
14 If a teacher wants to test her belief that more than five students in college classes typically receive A as a grade, she’ll perform
A. two-tail testing of a mean.
B. one-tail testing of a mean.
C. two-tail testing of a proportion.
D. one-tail testing of a proportion.
15. A woman and her son are debating about the average length of a preacher’s sermons on Sunday morning. Despite the mother’s arguments, the son thinks that the sermons are more than twenty minutes. For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05 level of significance, he wishes to determine whether he is correct in thinking that the average length of sermons is more than 20 minutes. What is the test statistic?
16. For 1996, the U.S. Department of Agriculture estimated that American consumers would have eaten, on average, 2.6 pounds of cottage cheese throughout the course of that year. Based on a longitudinal study of’98 randomly selected people conducted during 1996, the National Center for Cottage Cheese Studies found an average cottage cheese consumption of2.75 pounds and a standard deviation of s = 14 ounces. Given this information, which of the following statements would be correct concerning a two-tail test at the
0.05 level of significance?
A. We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.
B. We can conclude that we can’t reject the claim that the average cottage cheese consumption in America is 2.6 pounds per person per year.
C. We can conclude that the average cottage cheese consumption in America isn’t 2.6 pounds per person per year.
D. We can conclude that the average cottage cheese consumption in America is at least 0.705 pound more or less than 2.75 pounds per person per year.
17. A federal auditor for nationally chartered banks, from a random sample of 100 accounts, found that the average demand deposit balance at the First National Bank of Arkansas was $549.82. If the auditor needed a point estimate for the population mean for all accounts at this bank, what should he use?
A. There’s no acceptable value available.
R The auditor should survey the total of all accounts and determine the mean.
C. The average of $549.82 for this sample
D. The average of $54.98 for this sample
18. A random sample of 10 employees is selected from a large firm. For the 10 employees, the number of days each was absent during the past month was found to be 0, 2, 4, 2, 5, 1, 7, 3, 2, and 4. Ofthe following values, which would you use as the point estimate for the average number of days absent for all the firm’s employees?
19 H0 is p = 0.45 and His p ≠ 0.45. What type of test will be performed?
A. Two-tail testing of a proportion
B. One-tail testing of a mean
C. One-tail testing of a proportion
D. Two-tail testing of a mean
20. The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven’t really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?
A. H0:p ≥ 0.10 and H1:p<0.10
B.H 0:p ≤ 0.10 and H1:p > 0.10
C.H0:p = 0.10 and H : p ≠ 0.10
D. H0:p > 0.10 and H1 : p ≤ 0.10