Student: Brandy Freytag Date: 7/11/16 Instructor: Doug LeVeque, Beverly Wood Assignment: MSL Chapter 7 HW Course: MATH_211_1841_May_2016(LeVeque) 1. Two symbols are used for the mean: and x. a. Which represents a parameter and which a statistic? b. In determining the mean age of all students at your school, you survey 30 students and find the mean of their ages. Is this mean x or ? a. The symbol represents a parameter and x represents a statistic. b. The mean is x. 2. Explain the difference between sampling with replacement and sampling without replacement. Suppose you had the names of 10 students, each written on a 3 by 5 notecard, and want to select two names. Describe both procedures. Describe sampling with replacement. Choose the correct answer below. A. Draw a notecard, note the name, replace the notecard and draw again. It is not possible the same student could be picked twice. B. Draw a notecard, note the name, do not replace the notecard and draw again. It is possible the same student could be picked twice. C. Draw a notecard, note the name, do not replace the notecard and draw again. It is not possible the same student could be picked twice. D. Draw a notecard, note the name, replace the notecard and draw again. It is possible the same student could be picked twice. Describe sampling without replacement. Choose the correct answer below. A. Draw a notecard, note the name, replace the notecard and draw again. It is not possible the same student could be picked twice. B. Draw a notecard, note the name, do not replace the notecard and draw again. It is possible the same student could be picked twice. C. Draw a notecard, note the name, do not replace the notecard and draw again. It is not possible the same student could be picked twice. D. Draw a notecard, note the name, replace the notecard and draw again. It is possible the same student could be picked twice. 3. Marco is interested in whether Proposition P will be passed in the next election. He goes to the university library and takes a poll of 100 students. Since 55% favor Proposition P, Marco believes it will pass. Explain what is wrong with his approach. Choose the correct answer below. A. Marco took a convenience sample. The students may not be representative of the voting population, so the proposition may not pass. B. The proportion is too close to 50% for an accurate conclusion to be made. C. Marco took too small a sample. There were not enough students surveyed to determine for sure that the proposition will pass. 4. Shortly after Country C invaded Country A a website posed a question to readers of their magazine on the Internet: "Who really poses the greatest danger to world peace? Country A, Country B, or Country C?" The site received 706,617 responses: 6.3% said Country A, 6.4% said Country B, and 87.2% said Country C. Identify the population, and explain why the results might not reflect the true opinions of the population. Choose the correct answer below. A. The population of everyone on the Internet. B. The population of Country A, Country B, and Country C. C. The population of all readers of the magazine on the Internet. Choose the correct answer below. A. Because it was a voluntary-response sample, it could be that only people who were really angry with Country C took the time to respond. B. There were only 3 options so people might not be able to fully express their opinion. C. The order of the countries might bias the response. D. Because so many people responded it might be more than 10% of the population. 5. A teacher at a community college sent out questionnaires to evaluate how well the administrators were doing their jobs. All teachers received questionnaires, but only 10% returned them. Most of the returned questionnaires contained negative comments about the administrators. Explain how an administrator could dismiss the negative findings of the report. Choose the correct answer below. A. There is measurement bias. The questions could have been worded in such a way that the respondents responses were influenced. B. The entire population was surveyed and therefore inferences cannot be drawn. C. This was only one survey and people's opinions change over time. D. There is nonresponse bias. The results could be biased because the small percentage who chose to return the survey might be very different from the majority who did not return the survey. 6. a. If a rifleman's gunsight is adjusted incorrectly, he might shoot bullets consistently close to 2 feet left of the bull's-eye target. Draw a sketch of the target with the bullet holes. Does this show lack of precision or bias? b. Draw a second sketch of the target if the shots are both unbiased and precise (have little variation). The rifleman's aim is not perfect, so your sketches should show more than one bullethole. a. Draw a sketch of the target with the bullet holes consistently close to 2 feet left of the bull's-eye target. Choose the correct target below. Note that the diameter of the target is 8 feet. A. B. C. D. Does this show lack of precision or bias? A. Lack of precision B. Neither bias or lack of precision C. Both bias and lack of precision D. Bias b. Draw a second sketch of the target if the shots are both unbiased and precise. A. B. C. D. 7. A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8). a. Find the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. 5 5 1 5 4 1 8 0 7 7 7 3 2 5 1 1 3 4 0 9 7 5 9 3 9 8 0 0 5 1 b. Does the proportion found in part (a) represent p (the sample proportion) or p (the population proportion)? c. Find the error in this estimate, the difference between p and p (or p p). a. The given random number table consists of (Round to two decimal places as needed.) 70 % odd-numbered digits. b. Does the proportion found in part (a) represent p (the sample proportion) or p (the population proportion)? p (the sample proportion) p (the population proportion) c. Find the error in this estimate, the difference between p and p (or p p). Error = 20 % (Round to two decimal places as needed.) 8. According to a candy company, packages of a certain candy contain 22% orange candies. Suppose we examine 400 random candies. a. What value should we expect for our sample percentage of orange candies? b. What is the standard error? c. Use your answers to fill in the blanks below. We expect ____% orange candies, give or take _____%. a. We should expect (Type an integer or a decimal.) % of the candies in the sample to be orange. b. What is the standard error? SE = (Round to three decimal places as needed.) c. Use your answers to fill in the blanks below. We expect % orange candies, give or take (Round to one decimal place as needed.) %. 9. According to a candy company, packages of a certain candy contain 15% orange candies. Find the approximate probability that the random sample of 300 candies will contain 16% or more orange candies. Using a normal approximation, what is the probability that at least 16% of 300 randomly sampled candies will be orange? P p 0.16 = (Round to three decimal places as needed.) 10. Juries should have the same racial distribution as the surrounding communities. About 26% of residents in a certain region are a specific race. Suppose a local court randomly selects 50 adult citizens of the region to participate in the jury pool. Use the Central Limit Theorem (and the Empirical Rule) to find the approximate probability that the proportion of available jurors of the above specific race is more than three standard errors from the population value of 0.26. The conditions for using the Central Limit Theorem are satisfied because the sample is random; the population is more than 10 times 50; n times p is 13, and n times (1 minus p) is 37, and both are more than 10. Fill in the blanks below. Because the sampling distribution for the sample proportion is approximately normal, it is known that the probability of falling within three standard errors is about 0.997. Therefore, the probability of falling more than three standard errors away from the mean is about 0.003. 11. You have sent out 4000 invitations to hear a speaker, and you must rent chairs for the people who come. In the past, usually about 15% of the people invited have come to hear the speaker. Complete parts a through d below. a. On average, what proportion of those invited should we expect to attend? Expect of those invited to attend. (Type an integer or a decimal.) b. Suppose you assume that 15.5% of those invited will attend, and so you rent 620 chairs (because 0.155 times 4000 is 620). What is the approximate probability that more than 15.5% of those invited will show up and you will not have enough chairs? Refer to the TI-83/84 output given. Recall that this gives the Normal cumulative probability in the following format: Normalcdf (left boundary, right boundary, mean, standard deviation) normalcdf (0.155, 1 , 0.15, 0.00564579) 0.1879123368 Using a the output given above, what is the approximate probability that more than 15.5% of those invited will show up and you will not have enough chairs? (Round to four decimal places as needed.) Draw a well-labeled sketch of the Normal curve, and shade the appropriate region to represent the probability. A. B. 0.15 Area = 0.1879 0.13 0.155 0.17 C. 0.155 0.15 Area = 0.1879 0.13 0.15 D. 0.17 Area = 0.1879 0.13 0.155 0.17 0.155 Area = 0.1879 0.13 0.15 0.17 c. What is the approximate probability that more than 16% of the 4000 invited will show up? How many chairs would you have to rent if exactly 16% of those invited attended? Using a normal approximation, the probability that more than 16% of the 4000 invited will show up is P p 0.16 = . (Round to four decimal places as needed.) How many chairs would you have to rent if exactly 16% of those invited attended? chairs d. Why is your answer to part c smaller than your answer to part b? A. The answer to part c is smaller because 15.5% is farther out in the right tail than 16%, and it is the tail area that gives the probability of interest. B. The answer to part c is not smaller than the answer to part b. C. The answer to part c is smaller because 16% is farther out in the right tail than 15.5%, and it is the tail area that gives the probability of interest. D. The answer to part c is larger because 16% is farther out in the right tail than 15.5%, and it is the tail area that gives the probability of interest. 12. A true/false test has 60 questions. A passing grade is 57% or more correct answers. a. What is the probability that a person will guess correctly on one true/false question? b. What is the probability that a person will guess incorrectly on one question? c. Find the approximate probability that a person who is just guessing will pass the test. d. If a similar test were given with multiple-choice questions with four choices for each question, would the approximate probability of passing the test by guessing be higher or lower than the approximate probability of passing the true/false test? Why? a. What is the probability that a person will guess correctly on one true/false question? (Type an integer or a decimal.) b. What is the probability that a person will guess incorrectly on one question? (Type an integer or a decimal.) c. Find the approximate probability that a person who is just guessing will pass the test. Using a normal approximation, the probability that a person who is just guessing will pass the test is (Round to four decimal places as needed.) . d. If a similar test were given with multiple-choice questions with four choices for each question, would the approximate probability of passing the test by guessing be higher or lower than the approximate probability of passing the true/false test? Why? A. Higher, because the probability of guessing correctly on each question is higher when there are four options. B. Higher, because the probability of guessing correctly on each question is lower when there are four options. C. Lower, because the probability of guessing correctly on each question is lower when there are four options. D. Lower, because the probability of guessing correctly on each question is higher when there are four options. 13. A random sample of likely voters showed that 60% planned to vote for Candidate X, with a margin of error of 3 percentage points and with 95% confidence. a. Use a carefully worded sentence to report the 95% confidence interval for the percentage of voters who plan to vote for Candidate X. b. Is there evidence that Candidate X could lose? c. Suppose the survey was taken on the streets of a particular city and the candidate was running for president of the country that city is in. Explain how that would affect your conclusion. a. Which of the following statements best describes the confidence interval for the percentage of voters who plan to vote for Candidate X? A. I am 95% confident that the population percentage of voters not supporting Candidate X is between 57% and 63%. B. I am 95% confident that the population percentage of voters supporting Candidate X is between 57% and 63%. C. I am 95% confident that the population percentage of voters supporting Candidate X is between 60% and 63%. D. I am 95% confident that the population percentage of voters supporting Candidate X is between 57% and 60%. b. Is there evidence that Candidate X could lose? A. There is no evidence that the candidate could lose. The reason there is no evidence is because 60% of the sample voters planned to vote for Candidate X. B. There is evidence that the candidate could lose. The reason there is evidence is because the interval is entirely above 50%. C. There is evidence that the candidate could lose. The reason there is evidence is because the margin of error is 3%. D. There is no evidence that the candidate could lose. The reason there is no evidence is because the interval is entirely above 50%. c. Which of the following is the best explanation on how the survey would affect your conclusion? A. A sample from this particular city would not be representative of the entire country and would be helpful in this context. B. A sample from this particular city would not be representative of the entire country and would be worthless in this context. C. A sample from this particular city would be representative of the entire country and would be worthless in this context. D. A sample from this particular city would be representative of the entire country and would be helpful in this context. 14. In a simple random sample of 1500 young people, 87% had earned a high school diploma. Complete parts a through d below. a. What is the standard error for this estimate of the percentage of all young people who earned a high school diploma? (Round to four decimal places as needed.) b. Find the margin of error, using a 95% confidence level, for estimating the percentage of all young people who earned a high school diploma. % (Round to one decimal place as needed.) c. Report the 95% confidence interval for the percentage of all young people who earned a high school diploma. ( %, %) (Round to one decimal place as needed.) d. Suppose that in the past, 80% of all young people earned high school diplomas. Does the confidence interval you found in part c support or refute the claim that the percentage of young people who earn high school diplomas has increased? Explain. A. The interval supports this claim. This is because 80% is not in the interval, and all values are above 80%. B. The interval does not support this claim. This is because 80% is in the interval. C. The interval supports this claim. This is because 80% is in the interval. D. The interval does not support this claim. This is because 80% is not in the interval, and all values are above 80%. 15. In the fall of 2008, a country has a total of 100 government officials. Of the total number of government officials 23 were female. For the year 2008, find a 95% confidence interval for the percentage of government officials who were female or explain why you should not find a confidence interval for the percentage of government officials who were female in 2008. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The confidence interval is ( B. C. The proportion of , ). 23 is the population proportion, not a sample proportion. You should not 100 find a confidence interval unless you have a sample and are making statements about the population from which the sample has been drawn. The proportion of 23 is the sample proportion, not a population proportion. You should not 100 find a confidence interval unless you have a population and are making statements about the sample from which the population has been drawn. 16. A poll asked for people's opinion on whether closing local newspapers would hurt civic life; 425 of 1002 respondents said it would hurt civic life a lot. Complete parts a through d below. a. Find the proportion of the respondents who said that closing local papers would hurt civic life a lot. (Round to three decimal places as needed.) b. Find a 95% confidence interval for the population proportion who believed closing newspapers would hurt civic life a lot. Assume the poll used a simple random sample (SRS). (In fact, it used random sampling, but a more complex method than SRS.) ( , ) ( Round to three decimal places as needed.) c. Find an 80% confidence interval for the population proportion who believed closing newspapers would hurt civic life a lot. ( , ) ( Round to three decimal places as needed.) d. Which interval is wider and why? A. The 95% interval is wider. To get a higher degree of certainty, the interval needs to be widened. B. The 95% interval is wider. To get a higher degree of certainty, the interval needs to be widened just on the left side. C. The 80% interval is wider. To get a higher degree of certainty, the interval needs to be widened. D. The 95% interval is wider. To get a higher degree of certainty, the interval needs to be widened just on the right side. 17. In a 2008 survey, people were asked their opinions on astrology - whether it was very scientific, somewhat scientific, or not at all scientific. Of 1436 who responded, 76 said astrology was very scientific. a. Find the proportion of people in the survey who believe astrology is very scientific. b. Find a 95% confidence interval for the population proportion with this belief. c. Suppose a TV news anchor said that 5% of people in the general population think astrology is very scientific. Would you say that is plausible? Explain your answer. a. The proportion of people in the survey who believe astrology is very scientific is (Round to four decimal places as needed.) . b. Construct the 95% confidence interval for the population proportion with the belief that astrology is very scientific. ( , ) (Round to three decimal places as needed.) c. Choose the correct answer below. A. This is plausible because 5% is inside the interval. B. This is not plausible because 5% is outside the interval. C. This is not plausible because 5% is inside the interval. D. This is plausible because 5% is outside the interval. 18. Find the sample size required for a margin of error of 3.0 percentage points, and then find one for a margin of error of 1.5 percentage points; for both, use 95% confidence. Find the ratio of the larger sample size to the smaller sample size. To reduce the error by half, what do you need to multiply the sample size by? Use the shortcut formula n = 1 , where n represents the population size and m represents the margin of error in m2 decimal form, to find the necessary sample size required for a margin of error of 3.0 percentage points. n= (Round up to the nearest integer.) Find the necessary sample size required for a margin of error of 1.5 percentage points. n= (Round up to the nearest integer.) Use the populations obtained above to find the ratio of the larger sample size to the smaller sample size. (Type an integer or decimal rounded to the nearest hundredth as needed.) To reduce the error by half, what do you need to multiply the sample size by? (Type an integer or decimal rounded to the nearest hundredth as needed.) 19. Eric randomly surveyed 150 adults from a certain city and asked which team in a contest they were rooting for, either North High School or South High School. From the results of his survey, Eric obtained a 95% confidence interval of (0.52,0.68) for the proportion of all adults in the city rooting for North High. What proportion of the 150 adults in the survey said they were rooting for North High School? Choose the correct answer below. A. 0.60 B. 0.646 C. Somewhere between 0.52 and 0.68, but the exact proportion cannot be determined. D. This information cannot be determined from the information given in the problem. 20. Days before a presidential election, an article based on a nationwide random sample of registered voters reported the following statistic, "52% ( 3%) of registered voters will vote for Robert Smith." What is the " 3%" called? The " 3%" is called the (1) (1) sample proportion. margin of error. standard error. confidence interval for a proportion. 21. Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of 3%." The margin of error was based on a 95% confidence level. Can we say with 95% confidence that Robert Smith will win the election if he needs a simple majority of votes to win? Choose the correct answer below. A. Yes, since over 50% of the voters in the sample say they will vote for Robert Smith. B. Yes, because 50% is within the bounds of the confidence interval. C. No, because 50% is within the bounds of the confidence interval. D. No, because the margin of error can never be more than 1%. 22. Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of 3%." The margin of error was based on a 95% confidence level. Fill in the blanks to obtain a correct interpretation of this confidence interval. We are ___________ confident that the ___________ of registered voters ___________ planning on voting for Robert Smith is between ___________ and ___________. We are (1) confident that the (2) of registered voters (3) on voting for Robert Smith is between (4) (1) 90% (2) 95% and (5) average number percentage planning (3) in this sample (4) in the nation 100% 52% (5) 100%. 49% 52%. 50% 55%. 0% 50%. 23. Fill in the blank. The margin of error is _____________ the width of the confidence interval. The margin of error is (1) (1) twice the width of the confidence interval. half the same as one-fourth 95% of 24. An association of Realtors reports state-by-state median existing-home prices for each quarter. Why do you suppose they use the median instead of the mean? What might be the disadvantage of reporting the mean? Choose the correct answer below. A. Home prices are discrete data, and the median should always be reported instead of the mean for discrete data. Reporting the mean would have the disadvantage of being more difficult to interpret. B. Home prices probably have a symmetric distribution which makes the median a better representation of the center than the mean. Reporting the mean would give the impression that the "typical" home price is much lower or higher than it actually is. C. Home prices are probably skewed to the left and not symmetric. This makes the median a better representation of the center than the mean which would be influenced by the extremely low priced homes. Reporting the mean would give the impression that the "typical" home price is lower than it is. D. Home prices are probably skewed to the right and not symmetric. This makes the median a better representation of the center than the mean which would be influenced by the extremely high priced homes. Reporting the mean would give the impression that the "typical" home price is higher than it is. 25. A community college faculty is negotiating a new contract with the school board. The distribution of faculty salaries is skewed right by several faculty members who make over $100,000 per year. If the faculty want to give the community the impression that they deserve higher salaries, should they advertise the mean or median of their current salaries? Choose the correct answer below. A. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries. B. The faculty should use the median to make their argument. The median will be higher than the mean since the median is influenced by the few high salaries. C. The faculty should use the mean to make their argument. The mean will be higher than the median since the mean is influenced by the few extremely high salaries. D. The faculty should use the mean to make their argument. The mean will be lower than the median since it will be influenced by the few high salaries. 26. Identify when the interquartile range is better than the standard deviation as a measure of dispersion and explain its advantage. Choose the correct answer below. A. When the distribution is skewed left or right or contains some extreme observations, then the interquartile range is preferred since it is resistant. B. When the distribution is symmetric, then the interquartile range is preferred since it is easier to calculate. C. When the distribution is symmetric, then the interquartile range is preferred since it is resistant. D. When the distribution is skewed left or right or contains some extreme observations, then the interquartile range is preferred since it uses all the observations in its calculation