1) Suppose that = 155 and = 20. Find the score 2.2 standard deviations above the mean. 20 5 19 9 19 0 18 5 2) Suppose that = 155 and = 20. Find the score 2.8 standard deviations below the mean. 8 9 9 0 9 5 9 9 3) Two people are selected at random from 6 men and 9 women. The random variable is the number of men selected. Give all possible values of the random variable. 0,1,2,3 0,1,2 0,1,2,3 ,4 1,2,3 4) Identify the random variable as discrete or continuous: the volume of water in Lake Michigan. discrete continuous 5) Customers at a local were shopping mall were asked to state which of three brands of coffee tasted the best. The brands were numbered 1, 2, and 3. The results are summarized in the table. If the brand number is a random variable, does this define a probability distribution? Ye s No 6) When a new floral shop opened, a record of the daily number of phone calls was kept. The records showed the following data. Let the number of calls be the random variable X. Use this summary to determine the probability that the number of phone calls is 4 per day. 1/30 1/15 1/10 3/10 7/15 7) A U. S. History professor has a test bank of questions for a quiz on the United States presidency. The test bank has seven true-false questions, three discussion questions, and ten multiple choice questions. The computer randomly selects ten questions. Let the random variable X be the number of multiple choice questions. List the possible values of X. X ={1, 2, ..., 20} X ={1, 2, ..., 10} X ={0, 1, 2, 3, ..., 20} X ={0, 1, 2, 3, ..., 10} 8) A community bank studied the transaction times at the tellers' windows. They found that, rounded to the nearest minute, 15% of the transactions took one minute, 30% took two minutes, 25% took three minutes, 20% took four minutes, and 10% took five minutes. Find the expected time of a random transaction and round your answer to the tenths place. 2.8 minutes 3.8 minutes 4.8 minutes 5.8 minutes 9) Which of the following statement(s) is(are) a characteristic(s) of a binomial experiment? A. The experiment consists of 'n' identical trials. B. Each trial results in one of two outcomes, 'success' or 'failure'. C. The probability of success on a single trial is equal to 'p' and remains the same from trial to trial. The probability of failure is equal to q = (1 - p). D. The trials are independent. E. We are interested in 'x', the number of successes observed during the 'n' trials, for x = 0, 1, 2, ..., n. All of the above are characteristics of a binomial experiment. Only some of the above are characteristics of a binomial experiment. None of the above are characteristics of a binomial experiment. 10) The taste test for PTC (phenylthiourea) is a common class demonstration in the study of genetics. It is known that 70% of the American people are \"tasters\" with the rest are \"non-tasters\". Suppose a genetics class of size 20 does the test to see if they match the American percentage of \"tasters\" and \"non-tasters\". Assume that the assignment of students to classes is a random process. Calculate the mean. 3 6 7 1 4 11) From past experience, it is known that 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year-old children are given this voice recognition test. Calculate the variance. 0. 2 0. 9 1. 8 3. 9 12) A quiz consists of 30 questions. Each question has 3 answer choices with exactly one correct answer. A student is completely unprepared for the quiz, so he guesses on all 30 questions. How many questions should the student expect to answer correctly? 1 0 1 3 1 5 1 8 2 4 13) A quiz consists of 18 questions. Each question has 3 answer choices with exactly one correct answer. A student is completely unprepared for the quiz, so he guesses on all 18 questions. How many questions should the student expect to answer incorrectly? 6 8 9 1 2 1 8 14) It is known that 10% of the customers in an electronics store purchase an MP3 player. A random sample of 30 customers is selected. Assume that the customers' purchases are made independently. What is the definition of \"success\" in this binomial distribution application? A customer makes a purchase in this store. A customer purchases an MP3 player in this store. A customer does not make a purchase in this store. A customer does not purchase an MP3 player in this store. 15) It is known that 10% of the customers in an electronics store purchase an MP3 player. A random sample of 30 customers is selected. Assume that the customers' purchases are made independently. What is the probability of \"success\" in a single trial of this binomial distribution application? 10 % 30 % 50 % 70 % 90 % 16) It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes. A random sample of 25 customers is selected. Assume that the customers' purchases are made independently. In this binomial distribution application, which Excel statement will find the probability of exactly 5 customers purchasing a pair of running shoes? =BINOMDIST(5, 25, 70%,FALSE) =BINOMDIST(5, 25, 70%,TRUE) =1-BINOMDIST(5, 25, 70%,FALSE) =1-BINOMDIST(5, 25, 70%,TRUE) 17) A new surgical procedure is said to be successful 90% of the time. Suppose the procedure is performed five times. Assume that the results of each procedure are independent of one another. In this binomial distribution application, which Excel statement will find the probability of 2 or fewer successful surgical procedures? =1-BINOMDIST(2,5,90%,TRUE) =BINOMDIST(2,5,10%,FALSE) =BINOMDIST(2,5,90%,TRUE) =1-BINOMDIST(2,5,10%,FALSE) 18) It is known that 10% of the customers in an electronics store purchase an MP3 player. A random sample of 30 customers is selected. Assume that the customers' purchases are made independently. In this binomial distribution application, which Excel statement will find the probability of more than 10 customers who purchase an MP3 player in this electronics store? =1- BINOMDIST(10,30,10%,TRUE) =1-BINOMDIST(10,30,10%,FALSE) =BINOMDIST(10,30,10%,TRUE) =BINOMDIST(10,30,10%,FALSE) 19) Car color preferences change over the years and according to the particular model that the customer selects. In a recent year, 20% of all luxury cars sold were white. Assume that 25 cars of that year and type are randomly selected. In this binomial distribution application, which Excel statement will find the probability of between 7 and 10, inclusively, white luxury cars? =BINOMDIST(10,25,20%,TRUE)-BINOMDIST(6,25,20%,TRUE) =BINOMDIST(10,25,20%,FALSE)-BINOMDIST(7,25,20%,FALSE) =1-BINOMDIST(3,25,20%,TRUE) =1-BINOMDIST(7,10,20%,FALSE) 20) Which of the following statement(s) is(are) a characteristic(s) of the normal distribution? It is symmetric. It has a bell shape. The values of the mean, median, and mode are equal. All of the above are characteristics of a normal distribution. Only some of the above are characteristics of a normal distribution. None of the above are characteristics of a normal distribution. 21) 0 -1 1.25 Let = 150 and = 15. Find the z-score for the score, x = 135. 0.62 5 22) 16 7 17 6 18 9 15 8 Let = 160 and = 16. Find the score x if the z-score = 1. 23) What proportion of the data from a normal distribution is within one standard deviation from the mean? 0.95 44 0.68 26 0.47 72 0.51 18 0.87 33 24) The distribution of IQ scores for high school graduates is normally distributed with a mean of 102 and a standard deviation of 14. Identify the Excel statement that will find the probability that a person chosen at random from this group has an IQ score above 146. =1-NORMSDIST(3.142857143) =NORMSDIST(3.142857143) =1-NORMSDIST(146) =1-NORMSDIST(102) =NORMSDIST(146) 25) EPA studies of fuel consumption indicate compact car mileage to be normally distributed with a mean of 25.1 and a standard deviation of 6 mpg. Identify the Excel statement that will find the percentage of compact cars that get between 21 and 39 mpg. =[1-NORMSDIST(-0.683)-NORMSDIST(2.3167)]*100 =[NORMSDIST(21)-NORMSDIST(39)]*100 =[NORMSDIST(-0.683)-NORMSDIST(2.3167)]*100 =[NORMSDIST(-0.683)+NORMSDIST(2.3167)]*100 =[1-NORMSDIST(21)-NORMSDIST(39)]*100 26) Assume a normal distribution. The probability that a new drug will cure a certain disease is 0.6. It is administered to 100 patients. Find the probability that it will cure less than 75 patients. Round your percentage to the hundredths place. 98.3 % 89.8 % 99.92 % 95.65 % 27) Assume a normal distribution. A coin is tossed 100 times. Find the probability of 52 to 65 heads. Round your percentage to the hundredths place. 38.11 % 32.45 % 42.11 % 36.45 % 28) Which statement is correct? A. A point estimate is a single number that has been calculated to estimate the population parameter. B. A point estimate is an estimate of the range of values for which an unknown, but true sample statistic lies. C. A point estimate is a sample statistic such that the mean of all possible values equals the population parameter. D. A point estimate is the sum of an estimator's squared bias plus its variance. Statemen tA Statemen tB Statemen tC Statemen tD 29) Which statement is correct? A. An interval estimate is a sampling procedure that matches each unit from Population A to a corresponding unit from Population B. An interval estimate is an estimate of the range of values for which an unknown, but true sample statistic lies. C. An interval estimate is a sample statistic such that the mean of all possible values equals the population parameter the statistic seeks to estimate. D. An interval estimate is the sum of an estimator's squared bias plus its variance Statemen tA Statemen tB Statemen tC Statemen tD 30) A proportion of a college basketball team's season ticket holders renew their tickets for the next season. Let 'p' denote the true proportion of ticket holders who buy tickets again for the following season. A random sample of 125 ticket holders revealed 95 people plan on renewing their tickets. Find the point estimate for 'p'. 0.3157894 737 0.76 1.3157894 74 0.24 0.89 31) Which statement is correct? A. The Central Limit Theorem states that the sample mean is always equal to the population mean. B. The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal for sample sizes 30 and larger. C. The Central Limit Theorem states that the sample mean is always equal to the population mean for sample sizes larger than 30. D. The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal for population sizes 30 and larger. Statement A Statement B Statement C Statement D 32) Which of the following sample sizes will produce a sampling distribution of the mean that is approximately normal? 10 20 30 All of the above. 33) Consider a large population with a mean of 150 and standard deviation of 27. A random sample of size 36 is taken from the population. Calculate the standard error of the sampling distribution of this sample mean and round your answer to the hundredths place 4.1 7 4.5 0 5.4 0 5.5 6 34) Compute the margin of error in estimating a population mean for a sample size of 60 and a variance of 4. Round your answer to the thousandths place. 0.07 6 0.24 0 0.50 6 0.75 9 35) If the standard deviation of a population is known and we wish to estimate the population mean with 90% confidence, what is the appropriate critical value 'z' to use? 1.96 1.33 1.66 7 1.64 5 1.28 36) What does the interpretation of a 95% confidence interval estimate mean? If we repeatedly draw samples of the same size from the same population, 95% of the values of the sample means will result in a confidence interval that includes the population mean. There is a 95% probability that the population mean will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL). We are 95% confident that we have selected a sample whose range of values does not contain the population mean. There is a 5% probability that the population mean will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL). If we repeatedly draw samples of the same size from the same population, 5% of the values of the sample means will result in a confidence interval that includes the population mean. 37) A random sample of 44 salespersons were asked how long on average they were able to talk to a potential customer. Their answers revealed a mean of 8.500000000 with a variance of 6 minutes. Construct a 95% confidence interval for the time it takes a salesperson to talk to a potential customer. LCL = 7.176222033, UCL = 8.523777967 LCL = 7.276222033, UCL = 10.72377797 LCL = 8.376222033, UCL = 10.32377797 LCL = 7.776222033, UCL = 9.223777967 LCL = 8.276222033, UCL = 10.82377797 38) A random sample of 76 people revealed it took an average (mean) of 60 minutes with a standard deviation of 8 minutes for a person to complete a loan application at the bank. Construct a 90% confidence interval for the true time it takes any person to complete a loan form. LCL = 59.09044447, UCL = 62.60955553 LCL = 58.49044447, UCL = 61.50955553 LCL = 57.99044447, UCL = 63.00955553 LCL = 58.99044447, UCL = 63.10955553 LCL = 57.89044447, UCL = 60.80955553 39) A statistical test of hypothesis consists of the five parts below. Place the parts in order, beginning with the first part. a. State the conclusion. b. Calculate the test statistic and its p-value. c. Determine the alternate hypothesis. d. Determine the null hypothesis. e. Determine the rejection region. A, B, C, D, E D, C, A, B, E C, D, B, E, A D, C, B, E, A D, C, E, B, A 40) Complete the sentence: If we reject the null hypothesis, we conclude that _____ . there is not enough statistical evidence to infer that the alternative hypothesis is true there is not enough statistical evidence to infer that the null hypothesis is true the test must be repeated the test is statistically insignificant at the chosen level of significance 41) Which statement is an example of a null hypothesis? A. A particular industrial process manufactures windshields with an average length of 33 inches. B. The average quantity of detergent put into a box by a filling machine is not one pound. C. The shipping company's average delivery time is different from 3 days. D. The average thickness of an aluminum sheet is not 0.03 inches, as required. Statement A Statement B Statement C Statement D 42) A mail-order catalog claims that customers will receive their product within 3 days of ordering. A competitor believes this is an underestimate. State the appropriate null and alternative hypotheses to be tested by the competitor. Ho: u > 3 vs. Ha: u < 3, where u = the average number of days until the product is received Ho: u < 3 vs. Ha: u = 3, where u = the average number of days until the product is received. Ho: u = 3 vs. Ha: u > 3, where u = the average number of days until the product is received. Ho: u > 3 vs. Ha: u = 3, where u = the average number of days until the product is received. Ho: u = 3 vs. Ha: u < 3, where u = the average number of days until the product is received 43) A meteorologist claims that the average high temperature for the month of August in Philadelphia, PA. is 85 degrees Fahrenheit. If the residents of Philadelphia do not believe this to be true, what hypotheses should they test? Ho: u < 85 degrees Fahrenheit vs. Ha: u > 85 degrees Fahrenheit Ho: u > 85 degrees Fahrenheit vs. Ha: u < 85 degrees Fahrenheit Ho: u = 85 degrees Fahrenheit vs. Ha: u does not = 85 degrees Fahrenheit Ho: u = 85 degrees Fahrenheit vs. Ha: u > 85 degrees Fahrenheit Ho: u = 85 degrees Fahrenheit vs. Ha: u < 85 degrees Fahrenheit 44) The manufacturer of a particular battery pack for laptop computers claims its battery packs can function for 9 hours, on the average, before having to be recharged. A competitor claims that the manufacturer's claim is too high. A random sample of 38 battery packs was selected and placed on test. The mean functioning time before having to be recharged was 7.5 hours with a standard deviation of 1.6 hours. Perform the appropriate test of hypothesis to determine whether the competitor is correct. Test using alpha = 0.05. Calculate the test statistic and round your answer to the hundredths place. Test statistic = -2.05 Test statistic = -3.65 Test statistic = -7.31 Test statistic = -5.78 Test statistic = -1.29 45) The manufacturer of a particular battery pack for laptop computers claims its battery packs can function for 9 hours, on the average, before having to be recharged. A competitor claims that the manufacturer's claim is too high. A random sample of 37 battery packs was selected and placed on test. The mean functioning time before having to be recharged was 7.2 hours with a standard deviation of 1.8 hours. Perform the appropriate test of hypothesis to determine whether the competitor is correct. Test using alpha = 0.05. Based on the test statistic, what can you conclude? Test statistic = -6.082762530, so we should not reject the manufacturer's claim Test statistic = -37, so we should not reject the manufacturer's claim. Test statistic = -8.160882302, so we should reject the manufacturer's claim. Test statistic = -6.082762530, so we should reject the manufacturer's claim Test statistic = -37, so we should reject the manufacturer's claim. 46) A sample size of 150 is to be used to test the hypotheses H0: = 8.3 vs. Ha: 8.3 where is the true average weight of a newborn American baby. Determine the appropriate rejection region with a significance level of alpha = 0.05. Reject H0 if z >2.58 or z < -2.58 Reject H0 if z <2.58 and z > -2.58 Reject H0 if z >1.96 or z < -1.96 Reject H0 if z <1.96 and z > -1.96 Reject H0 if z >1.645 or z < -1.645 Reject H0 if z <1.645 and z > -1.645 47) A sample size of 80 is to be used to test the hypotheses H0: = 29 vs. Ha: > 29 where is the true average age of a person when he/she gets married. Determine the appropriate rejection region with a significance level of alpha/2 = 0.01. Reject H0 if z >2.33 Reject H0 if z >2.58 Reject H0 if z >1.645 Reject H0 if z >1.28 48) In a hypothesis test, the test statistic was calculated to be 2.76. The rejection region is -2.33 < z < 2.33. Which statement is true? The null hypothesis is accepted to be true The null hypothesis is rejected since the test statistic is outside the rejection region. The null hypothesis is not rejected since the test statistic is outside the rejection region. The null hypothesis is rejected since the test statistic proves it to be false 49) When the alternative hypothesis is formulated in a large-sample statistical test as > 0 or < 0, then your large-sample statistical test is a One-tailed test Two-tailed test Type I test Type II test 50) What are the two types of errors that can be made in hypothesis testing? Exception and Rejection Type I and Type II Analytical and Iterative Propogation and Human Error