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A sample space consists of 46 separate events that are equally likely. What is the probability of each? 1/46 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? 7/8 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. 5/6 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.) 0.6 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. 0.587 The probability that Luis will pass his statistics test is 0.94. Find the probability that he will fail his statistics test. 0.06 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. The series closer to the theoretical 50/50 cannot be determined unless the total number of rolls for both series is given. In a poll, respondents were asked whether they had ever been in a car accident. 220 respondents indicated that they had been in a car accident and 370 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth. 0.373 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 0.7 The distribution of B.A. degrees conferred by a local college is listed below, by major. MajorFrequency 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? 0.8200 Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see? 4 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? 24 A study of two types of weed killers was done on two identical weed plots. One weed killer killed 15% more weeds than the other. This difference was significant at the 0.05 level. What does this mean? The probability that one weed killer performed better by chance alone is less than 0.05 . 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? -$0.50 A class consists of 50 women and 82 men. If a student is randomly selected, what is the probability that the student is a woman? 50/132 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? There is less than a 0.01 chance that the first group's grades were better by chance alone. 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. 10,000 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. The variation in the x variable is a direct cause of the variation in the y variable. Eleven female college students are selected at random and asked their heights. The heights (in inches) are as follows: 67, 59, 64, 69, 65, 65, 66, 64, 62, 64, 62 Estimate the mean height of all female students at this college. Round your answer to the nearest tenth of an inch if necessary. 64.3 inches 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? 0.8849 Sample size = 400, sample mean = 44, sample standard deviation = 16. What is the margin of error? 1.6 Which line of the three shown in the scatter diagram below fits the data best? C 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. 0.26 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. 0.0425 Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram. -0.9 Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram. 0.9 A psychologist claims that more than 29 percent of the professional population suffers from problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in non-technical terms. There is not sufficient evidence to support the claim that the true proportion is greater than 29 percent. z = 1.8 for Ha: µ > claimed value. What is the P-value for the test? 0.0359 A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16-ounce bottles, µ, is less than 16.1 ounces? Perform the appropriate hypothesis test using a significance level of 0.10. Assume that = 0.9 ounces. The z of -1.49 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. Formulate the null and alternative hypotheses for the study described. Ho: µ = 18.4 hours H a: µ < 18.4 hours A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis? 97.5% 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? 25, 30 or 55 peanuts 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 null and alternative hypotheses for the test described. H0: µ = 16 ounces Ha: µ ¹ 16 ounces In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: H0 : µ = 9.8 hours Ha : µ > 9.8 hours Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased. Type I error In 1990, the average duration of long-distance telephone calls originating in one town was 9.3 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.3 minutes. Formulate the null and alternative hypotheses for the study described. Ho: µ = 9.3 minutes Ha: µ ¹ 9.3 minutes without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion. Ha is not supported; x̄ is less than 1 standard deviation above the claimed mean. A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed. State the null and alternative hypotheses for this test. A golfer wished to find a ball that would travel more than 160 yards when hit with his 7 -iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 8 times at the required speed. H0: µ < 170; Ha: µ = 170 Data from this test resulted in a sample mean of 163.2 yards with a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer's requirements. Use the partial t-table below to solve this problem. Do not reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 160 yards. Which of the following statements is true? The t distribution cannot be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population. A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2. What is the margin of error? 4.8 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. Smaller. E decreases as the square root of the sample size gets larger. 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 Total Colorblind Male Female Total 8 2 10 52 38 90 60 40 100 State the null and alternative hypothesis for the test associated with this data. H0: Colorblindness and gender are independent characteristics. Ha: Colorblindness and gender are related in some way. One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The critical value of X 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 4.613, state your conclusion about the relationship between gender and colorblindness. Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related. Lesson 3 Exam Question 1 5 / 5 points The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Find the median of the data. 3.45 in. Question 2 5 / 5 points The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score 533 drops the seminar and is replaced by a student with a score of 765. What will happen to the mean and the median scores of the class? Both the median and the mean will increase. Question 3 5 / 5 points The number of vehicles passing through a pharmacy drive-up line with two windows during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a fifteen-minute period. 16 8 24 22 30 19 18 27 11 15 17 24 26 23 7 25 21 16 20 14 19.5 Question 4 0 / 5 points The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the cars it makes. Suppose that the models and mpg's for a manufacturer are Corsair (31 mpg), Futura (30 mpg), Retro (37 mpg), and Envy (44 mpg). Twenty percent of the cars sold are Corsairs, 30% are Futuras, 40% are Retros, and 10% are Envys. Find the average mpg for this manufacturer. Question options: 35.5 mpg 34.0 mpg 34.4 mpg None of the above Question 5 5 / 5 points Suppose that your income is at the 81st percentile of wage earners in the United States. What percent of wage earners make more than you do? 19% Question 6 5 / 5 points The grocery expenses for six families were $80.86, $47.74, $57.92, $81.08, $75.18, and $88.08. Compute the mean grocery bill. Round your answer to the nearest cent. $71.81 Question 7 5 / 5 points Find the mode(s) for the given sample data. 20, 49, 46, 43, 49, 43, 49, 20, 22 49 Question 8 0 / 5 points A softball player has a batting average of exactly .300 and no more than 60 times at bat. Suppose this player gets 5 hits in her next 6 times at bat. What is the highest possible average she could now have? Question options: .500 .833 .348 There is insufficient information to answer the question Question 9 5 / 5 points The weights (in ounces) of 21 cookies are shown. Find the median weight. 0.62 1.25 0.60 1.62 0.75 0.74 1.35 1.25 1.53 0.99 0.62 1.25 1.28 0.66 0.47 1.25 0.74 1.28 1.72 0.75 0.56 Question options: 0.99 ounces Question 10 5 / 5 points The following data set is the GPAs of the students in a statistics class. 1.93, 1.99, 2.00, 2.04, 2.12, 2.34, 2.55, 2.55, 2.75, 2.75, 2.80, 2.80, 2.85, 3.02, 3.12, 3.22, 3.31, 3.33, 3.45, 3.69 What percentile is a GPA of 2.34? Question options: About the 30th Question 11 0 / 5 points The batting averages of the first three batters in the Eureka College women's softball team lineup are .310, .301, and .277. If the first three batters are considered as the "lead -off group", what is the batting average of the group? Question options: .301 .296 There is insufficient information to answer the question None of the above Question 12 5 / 5 points Use the range rule of thumb to approximate the standard deviation. 22,29, 21, 24, 27, 28, 25, 38 4.25 Question 13 5 / 5 points Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 15, 42, 53, 7, 9, 12, 14, 28, 47 Question options: 17.8 Question 14 5 / 5 points Find the mode(s) for the given sample data. 7.29, 7.41, 7.56, 7.29, 7.88, 7.99, 7.62 7.29 Question 15 5 / 5 points Suppose that there are 400 students in your school class. What class rank is the 20th percentile? 80 Question 16 0 / 5 points The host of a dinner party purchases wine based on the weighted average of clarity (10%), bouquet (5%), friendliness to the palate (5%), storage ability of opened bottles (40%), and price (40%). Suppose that Bone Ranch Wave has scores in these categories of 4, 5, 3, 8, and 9, respectively. What is its rating? Question options: 5.80 5.00 7.60 None of the previous Question 17 5 / 5 points Use the range rule of thumb to approximate the standard deviation. 496,598, 503, 528, 565, 601, 576, 543 26.25 Question 18 5 / 5 points Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 22, 29, 21, 24, 27, 28, 25, 36 4.8 Question 19 5 / 5 points Consider the distribution of heights of all the players in the National Basketball Association. What would you expect the shape of the distribution to be? Skewed left Question 20 5 / 5 points Al and Joe are two county sheriff's deputies assigned to watch for traffic violations. Their arrest and conviction records for May and June are shown below. Who had the best conviction percentage in May? Joe