Chapter 18 - 20 Exam MC Review Name_______________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the Normal model may be used to describe the distribution of the sample proportions. If the Normal model may be used, list the conditions and explain why each is satisfied. If Normal model may not be used, explain which condition is not satisfied. 1) A candy company claims that 25% of the jelly beans in its spring mix are pink. Suppose that the 1) candies are packaged at random in small bags containing about 300 jelly beans. A class of students opens several bags, counts the various colors of jelly beans, and calculates the proportion that are pink in each bag. Is it appropriate to use a Normal model to describe the distribution of the proportion of pink jelly beans? A) A Normal model is not appropriate because the population distribution is not Normal. B) A Normal model is not appropriate because the randomization condition is not satisfied: the 300 jelly beans in the bag are not a simple random sample and cannot be considered representative of all jelly beans. C) A Normal model is appropriate: Randomization condition is satisfied: the 300 jelly beans in the bag are selected at random and can be considered representative of all jelly beans 10% condition is satisfied: the sample size, 300, is less than 10% of the population of all jelly beans. success/failure condition is satisfied: np = 75 and nq = 225 are both greater than 10 D) A Normal model is not appropriate because the success/failure condition is not satisfied: np = 75 and nq = 225 neither of which is less than 10 E) A Normal model is not appropriate because the 10% condition is not satisfied: the sample size, 300, is larger than 10% of the population of all jelly beans.
Answer the question. 2) In a large class, the professor has each person toss a coin 200 times and calculate the proportion of his or her tosses that were tails. The students then report their results, and the professor records the proportions. One student claims to have tossed her coin 200 times and found 58% tails. What do you think of this claim? Explain your response. A) This is a typical result. Her proportion is only 1.60 standard deviations above the mean. B) This is a typical result. Her proportion is only 2.26 standard deviations above the mean. C) This is a fairly unusual result. Her proportion is about 1.60 standard deviations above the mean. D) This is an unusual result. Her proportion is about 2.26 standard deviations above the mean. E) This is an extremely unlikely result. Her proportion is about 5.2 standard deviations above the mean. Find the standard deviation of the sample proportion. 3) A candy company claims that its jelly bean mix contains 20% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 330 jelly beans. Find the mean of the proportion of blue jelly beans in a bag. A) = 2.8% B) = 2.2% C) = 0.9% D) = 0.20% E) = 20%
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Provide an appropriate response. 4) A certain population is strongly skewed to the right. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one? I. The distribution of our sample data will be closer to normal. II. The sampling model of the sample means will be closer to normal. III. The variability of the sample means will be greater. A) II only B) II and III only C) I only D) I and III only E) III only
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In a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tosses that come up heads. The students then report their results, and the professor plots a histogram of these proportions. Use the 68-95-99.7 Rule to provide the appropriate response. 5) If each student tosses the coin 200 times, about 95% of the sample proportions should be between 5) what two numbers? A) 0.071 and 0.106 B) 0.495 and 0.505 C) 0.429 and 0.571 D) 0.025 and 0.975 E) 0.2375 and 0.7375
Provide an appropriate response. 6) Which of the following describe how the sampling distribution model for the sample mean changes as the sample size is increased? A: The sampling distribution model becomes more Normal in shape B: The standard deviation of the sampling distribution gets smaller C: The mean of the sampling distribution gets smaller A) A and B B) A, B, and C C) B and C D) B only E) A only
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Find the specified probability, from a table of Normal probabilities. Assume that the necessary conditions and assumptions are met. 7) Assume that 25% of students at a university wear contact lenses. We randomly pick 200 students. 7) What is the probability that more than 28% of this sample wear contact lenses? A) 0.673 B) 0.327 C) 0.980 D) 0.164 E) 0.837
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Provide an appropriate response. 8) A certain population is bimodal. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one? I. The distribution of our sample data will be more clearly bimodal. II. The sampling distribution of the sample means will be approximately normal. III. The variability of the sample means will be smaller. A) II only B) II and III C) I, II, and III D) I only E) III only Solve the problem. 9) One hospital has found that 13.95% of its patients require specially equipped beds. If the hospital has 258 beds, what percentage of the beds should be specially equipped if the hospital wishes to be "pretty sure" of having enough of these beds? Assume that the hospital wants only a 5% chance that they could run short of these beds, even when the hospital is fully occupied. A) 17.5% B) 21.9% C) 19.5% D) 19.0% E) 18.2% 10) At a shoe factory, the time taken to polish a finished shoe has a mean of 3.7 minutes and a standard deviation of 0.48 minutes. If 44 shoes are polished, there is a 5% chance that the mean time to polish the shoes is below what value? A) 3.51 minutes B) 3.89 minutes C) 3.58 minutes D) 3.82 minutes E) 3.53 minutes
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Determine whether the Normal model may be used to describe the distribution of the sample means. If the Normal model may be used, list the conditions and explain why each is satisfied. If Normal model may not be used, explain which condition is not satisfied. 11) A researcher believes that scores on an IQ test for students at a certain college are skewed to the 11) left with a mean of 72 and a standard deviation of 15. The college has a total of 850 students. The researcher selects 200 students at random and determines the mean test score, x, for the students in the sample. May the Normal model be used to describe the sampling distribution of the mean, x? A) No, Normal model may not be used. 10% condition is not satisfied : the 200 students in the sample represent more than 10% of students at the college. This means that the independence assumption will not be satisfied. B) Yes, Normal model may be used. Randomization condition: The students were selected at random Independence assumption: It is reasonable to think that scores of randomly selected students are mutually independent. Large enough sample condition: a sample of 200 is certainly large enough, whatever the distribution of the scores in the original population 10% condition is satisfied since the 200 students represent more than 10% of students at the college. C) No, Normal model may not be used. Large enough sample condition is not satisfied: since the original population is skewed to the left, 200 is not a large enough sample D) No, Normal model may not be used since scores for students at the college are not normally distributed E) No, Normal model may not be used. Randomization condition is not satisfied since the 200 students in the sample may not be representative of all students at the college.
Describe the indicated sampling distribution. 12) The weights of people in a certain population are normally distributed with a mean of 158 lb and a standard deviation of 25 lb. Describe the sampling distribution of the mean for samples of size 9. In particular, state whether the distribution of the sample mean is normal or approximately normal and give its mean and standard deviation. A) Normal, mean = 158 lb, standard deviation = 2.78 lb B) Normal, mean = 158 lb, standard deviation = 25 lb C) Approximately normal, mean = 158 lb, standard deviation = 2.78 lb D) Normal, mean = 158 lb, standard deviation = 8.33 lb E) Approximately normal, mean = 158 lb, standard deviation = 8.33 lb
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At a large university, students have an average credit card debt of $2500, with a standard deviation of $1200. A random sample of students is selected and interviewed about their credit card debt. Use the 68-95-99.7 Rule to answer the question about the mean credit card debt for the students in this sample. 13) If we imagine all the possible random samples of 250 students at this university, 68% of the 13) samples should have means between what two numbers? A) $2272.33 and $2727.67 B) $1300 and $3700 C) $2424.11 and $2575.89 D) $2424.11 and $2651.78 E) $2348.22 and $2651.78
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Find the specified probability, from a table of Normal probabilities. Assume that the necessary conditions and assumptions are met. 14) The number of hours per week that high school seniors spend on homework is normally 14) distributed, with a mean of 11 hours and a standard deviation of 3 hours. 70 students are chosen at random. Let y represent the mean number of hours spent on homework for this group. Find the probability that y is between 10.2 and 11.5. A) 0.1383 B) 0.9048 C) 0.8371
D) 0.171
E) 0.0698
15) A restaurant's receipts show that the cost of customers' dinners has a skewed distribution with a mean of $54 and a standard deviation of $18. What is the probability that the next 100 customers will spend a total of less than $5000 on dinner? A) 0.5879 B) 0.9868 C) 0.4121 D) 0.0132 E) 0.9614
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16) The weights of the fish in a certain lake are normally distributed with a mean of 13 lb and a standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean weight will be between 10.6 and 16.6 lb? A) 0.0968 B) 0.6730 C) 0.3270 D) 0.5808 E) 0.4032
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Provide an appropriate response. 17) A researcher selects samples of size n from a population and determines the mean test score for each sample. The mean and standard deviation of the sampling distribution are 60 and 12 respectively. If the sample size is multiplied by a factor of 4, what will the mean and standard deviation of the new sampling distribution be? A) mean will be 30, standard deviation will be 6 B) mean will be 30, standard deviation will be 3 C) mean will be 60, standard deviation will be 3 D) mean will be 60, standard deviation will be 24 E) mean will be 60, standard deviation will be 6 Find the indicated probability. 18) You pay $10 and roll a die. If you get a five or six, you win $30. If not, you get to roll again. If you get a 5 or 6 on the second roll, you get your $10 back. Suppose you play this game 30 times. What's the probability that your mean winnings are more than $5? A) 0.1234 B) 0.0885 C) 0.1492 D) 0.2546 E) 0.4168 Provide an appropriate response. 19) A certain population is strongly skewed to the left. We want to estimate its mean, so we collect a sample. Which should be true if we use a large sample rather than a small one? I. The distribution of our sample data will be more clearly skewed to the left. II. The sampling model of the sample means will be more skewed to the left. III. The variability of the sample means will greater. A) II only B) I only C) I and III only D) III only E) II and III only
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Find the margin of error for the given confidence interval. 20) A survey found that 69% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of error for this survey if we want 90% confidence in our estimate of the percent of American adults who approve of cloning endangered animals. A) 2.83% B) 2.38% C) 5.09% D) 4.27% E) 24.35%
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Use the given degree of confidence and sample data to construct a confidence interval for the population proportion. 21) A study involves 638 randomly selected deaths, with 27 of them caused by accidents. Construct a 21) 98% confidence interval for the percentage of all deaths that are caused by accidents. A) (2.37%, 6.09%) B) (2.92%, 5.55%) C) (2.67%, 5.79%) D) (2.18%, 6.29%) E) (3.0%, 5.4%) Solve the problem. 22) A manufacturer wishes to estimate the proportion of washing machines leaving the factory that is defective. How large a sample should she check in order to be 90% confident that the true proportion is estimated to within 1.2%? A) 11,512 B) 9,393 C) 4,704 D) 6,670 E) Not enough information is given. 23) A survey of shoppers is planned to see what percentage use credit cards. Prior surveys suggest 50% of shoppers use credit cards. How many randomly selected shoppers must we survey in order to estimate the proportion of shoppers who use credit cards to within 1% with 95% confidence? A) 19,208 B) 9604 C) 8644 D) 6761.2 E) 16,577 What confindence level did the pollsters use? 24) A poll of 2017 likely voters indicated that 70% would vote in favor of a proposed constitutional amendment. The margin of error for this poll was 2%. A) 98% B) 99% C) 95% D) 90% E) Not enough information is given. Provide an appropriate response. 25) In a poll of 861 voters in a certain city, 72% said that they backed a bill which would limit growth and development in their city. The margin of error in the poll was reported as 3 percentage points (with a 95% degree of confidence). Make a statement about the adequacy of the sample size for the given margin of error. A) For the given sample size, the margin of error should be smaller than stated B) The reported margin of error is consistent with the sample size. C) The sample size is too small to achieve the stated margin of error. D) The sample size is too large to achieve the stated margin of error. E) There is not enough information to determine whether the margin of error is consistent with the sample size.
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 26) A newspaper article reported that a poll based on a sample of 800 voters showed the President's job approval rating stood at 62%. They claimed a margin of error of ± 3%. What level of confidence were the pollsters using?
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 27) We have calculated a confidence interval based on a sample of n = 180. Now we want to get a better estimate with a margin of error only one third as large. We need a new sample with n at least... A) 1620 B) 312 C) 20 D) 540 E) 60
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28) A relief fund is set up to collect donations for the families affected by recent storms. A random sample of 400 people shows that 28% of those 200 who were contacted by telephone actually made contributions compared to only 18% of the 200 who received first class mail requests. Which formula calculates the 95% confidence interval for the difference in the proportions of people who make donations if contacted by telephone or first class mail? (0.23)(0.77) A) (0.28 - 0.18) ± 1.96 400
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B) (0.28 - 0.18) ± 1.96
(0.23)(0.77) (0.23)(0.77) + 200 200
C) (0.28 - 0.18) ± 1.96
(0.28)(0.72) (0.18)(0.82) + 200 200
D) (0.28 - 0.18) ± 1.96
(0.28)(0.72) (0.18)(0.82) + 400 400
E) (0.28 - 0.18) ± 1.96
(0.23)(0.77) 200
29) We have calculated a 95% confidence interval and would prefer for our next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, we can I. change the z * value to a smaller number. II. take a larger sample. III. take a smaller sample. A) III only B) II only
C) I and III
D) I only
E) I and II
30) We have calculated a confidence interval based upon a sample of n = 200. Now we want to get a better estimate with a margin of error only one fifth as large. We need a new sample with n at least... A) 40 B) 1000 C) 5000 D) 450 E) 240
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Write the null and alternative hypotheses you would use to test the following situation. 31) At a local university, only 62% of the original freshman class graduated in four years. Has this percentage changed? A) H0 : p = 0.62 H A: p
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0.62
B) H0 : p < 0.62
HA: p > 0.62 C) H0 : p 0.62 HA: p = 0.62
D) H0 : p = 0.62
HA: p < 0.62 E) H0 : p < 0.62 HA: p = 0.62
32) A new manager, hired at a large warehouse, was told to reduce the 26% employee sick leave. The manager introduced a new incentive program for employees with perfect attendance. The manager decides to test the new program to see if it's better. What are the null and alternative hypotheses? A) H0 : p = 0.26 H A: p
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0.26
B) H0 : p < 0.26
HA: p = 0.26
C) H0 : p = 0.26
HA: p < 0.26
D) H0 : p > 0.26 HA: p < 0.26 E) H0 : p = 0.26
HA: p > 0.26
Provide an appropriate response. 33) The county health department has concerns about the chlorine level of 0.4% mg/mL at a local water park increasing to unsafe level. The water department tests the hypothesis that the local water park's chlorine proportions have remained the same, and find a P-value of 0.005. Provide an appropriate conclusion A) We can say there is a 0.5% chance of seeing a change in the chlorine proportions in the results we observed from natural sampling variation. We conclude the chlorine proportion is higher. B) There's only a 0.5% chance of seeing no change in the chlorine proportion in the results we observed from natural sampling variation. We conclude the chlorine proportion is higher. C) There is a 99.5% chance of no change in the chlorine proportion. D) There is a 0.5% chance of no change in the chlorine proportion. E) We can say there is a 0.5% chance of seeing no change in the chlorine proportions in the results we observed from natural sampling variation. There is no evidence of a higher chlorine proportion, but we cannot conclude the chlorine proportion is the same.
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34) In a test of H0 : µ = 8 versus Ha : µ 8, a sample of size 220 leads to a p-value of 0.034. Which of the
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following must be true? A) The null hypothesis should not be rejected at the 5% level. B) A 95% confidence interval for µ calculated from these data will not include µ = 8. C) At the 5% level if H0 is rejected, the probability of a Type II error is 0.034.
D) The sample size is insufficient to draw a conclusion with 95% confidence. E) A 95% confidence interval for µ calculated from these data will be centered at µ = 8.
Create a 95% confidence interval for the given data. 35) Data in 1980 showed that about 48% of the adult population had never smoked cigarettes. In 2004, a national health survey interviewed a random sample of 5000 adults and found that 54% had never been smokers. Create a 95% confidence interval for the proportion of adults (in 2004) who had never been smokers. A) Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 46.6% and 49.4%. B) Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 40% and 60%. C) Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 37.4% and 49.4%. D) Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 46.6% and 63.2%. E) Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 58.2%. Provide an appropriate response. 36) A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%. Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed. A) H0 : p = 0.04; HA: p 0.04; z = 1.07; P-value = 0.2846. This data does not show that more than 4% of students are retained; the university should not continue with the new programs. B) H0 : p = 0.04; HA: p > 0.04; z = -1.07; P-value = 0.1423. This data does not show that more
than 4% of students are retained; the university should not continue with the new programs. C) H0 : p = 0.04; HA: p < 0.04; z = 1.07; P-value = 0.8577. This data shows that more than 4% of students are retained; therefore, the university should continue with the new programs. D) H0 : p = 0.04; HA: p < 0.04; z = -1.07; P-value = 0.8577. This data shows that more than 4% of
students are retained; the university should continue with the new programs. E) H0 : p = 0.04; HA: p > 0.04; z = 0.96; P-value = 0.1685. This data does not show that more than 4% of students are retained; the university should not continue with the new programs.
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37) The federal guideline for smog is 12% pollutants per 10,000 volume of air. A metropolitan city is trying to bring its smog level into federal guidelines. The city comes up with a new policy where city employees are to use city transportation to and from work. A local environmental group does not think the city is doing enough, and that the pollution percentage is greater than 12%. An independent agency hired by the city to run a test used a random sample size of 250 and found the pollutants at 15%. Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed. A) H0 : p = 0.12; HA: p < 0.12; z = -1.56; P-value = 0.9406. This data shows a change of 12%
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pollutants in the air; the city should continue programs. B) H0 : p = 0.12; HA: p > 0.12; z = -1.56; P-value = 0.0594. This data does not show a change of
12% pollutants in the air; the city should change and increase programs. C) H0 : p = 0.12; HA: p > 0.12; z = 1.46; P-value = 0.0721. This data does not show a change of 12% pollutants in the air; the city should change and increase programs. D) H0 : p = 0.12; HA: p > 0.12; z = 1.56; P-value = 0.0594. This data does not show a change of 12% pollutants in the air; the city should change and increase programs. E) H0 : p = 0.12; HA: p < 0.12; z = 1.56; P-value = 0.9406. This data shows a change of 12% pollutants in the air; the city should continue with programs.
38) The U.S. Department of Labor and Statistics released the current unemployment rate of 5.3% for the month in the U.S. and claims the unemployment has not changed in the last two months. However, the states statistics reveal that there is a decrease in the U.S. unemployment rate. A test on unemployment was done on a random sample size of 1000 and found unemployment at 3.8%. Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed. A) H0 : p = 0.053; HA: p > 0.053; z = -2.12; P-value = 0.983. This data does not show that the unemployment rate has decreased in the last two months. B) H0 : p = 0.053; HA: p 0.053; z = -2.12; P-value = 0.034. This data shows that the
unemployment rate has decreased in the last two months. C) H0 : p = 0.053; HA: p < 0.053; z = 2.12; P-value = 0.017. This data does not show that the unemployment rate has decreased in the last two months. D) H0 : p = 0.053; HA: p > 0.053; z = 2.12; P-value = 0.983. This data shows that the unemployment rate has decreased in the last two months. E) H0 : p = 0.053; HA: p < 0.053; z = -2.12; P-value = 0.017. This data shows that the unemployment rate has decreased in the last two months.
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39) An online catalog company wants on-time delivery for at least 90% of the orders they ship. They have been shipping orders via UPS and FedEx but will switch to a more expensive service (ShipFast) if there is evidence that this service can exceed the 90% on-time goal. As a test the company sends a random sample of orders via ShipFast, and then makes follow-up phone calls to see if these orders arrived on time. Which hypotheses should they test? A) H0 : p < 0.90
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HA: p = 0.90
B) H0 : p = 0.90
HA: p < 0.90
C) H0 : p = 0.90
HA: p > 0.90 D) H0 : p = 0.90 HA: p 0.90
E) H0 : p > 0.90
HA: p = 0.90
40) A pharmaceutical company investigating whether drug stores are less likely than food markets to remove over-the-counter drugs from the shelves when the drugs are past the expiration date found a P-value of 2.8%. This means that: A) 97.2% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date than drug stores. B) There is a 2.8% chance the drug stores remove more expired over-the-counter drugs. C) 2.8% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date. D) There is a 97.2% chance the drug stores remove more expired over-the-counter drugs. E) None of these.
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Answer Key Testname: AP STATS CH 18-20 REVIEW WORKSHEET 2016
1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25)
C D B A C A D C A C A D C B D B E A B B A C B C B
26) Since ME = z *
27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40)
^^
pq , we have z * = n
0.03 (0.62)(0.38) 800
1.75
P(-1.75 < z < 1.75) = 92%. A C B C A C B B A E C E C E
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