their contents. If the sample mean is 15.2 oz. and the sample standard deviation is 0.50 oz., find the 95% confidence interval of the true mean.

Transcription

1 Math 1342 Exam 3-Review Chapters 7-9 HCCS **************************************************************************************** Name Date ********************************************************************************************** MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A sample of 35 different payroll departments found that employees worked an average of days a year. If the population standard deviation is 18.8 days, find the 90% confidence interval for the average number of days μ worked by all employees who are paid through payroll departments. A) < μ < B) < μ < C) < μ < D) < μ < ) 2) Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation for the population of 3.9 minutes. Jennifer's margin of error would be 1.4 minutes. A) False B) True 2) 3) Identify the degree of confidence displayed in the confidence interval shown below. 3) A) 90% B) 99% C) 95% D) 98% 4) Find t α/2 when n = 12 for the 95% confidence interval for the mean. A) 1.52 B) 2.20 C) 2.92 D) ) 5) A food snack manufacturer samples 11 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz. and the sample standard deviation is 0.50 oz., find the 95% confidence interval of the true mean. A) 14.1 < μ < 16.3 B) 15.0 < μ < 15.4 C) 14.9 < μ < 15.5 D) 12.9 < μ < ) Page 1

2 6) The following display from a TI-84 Plus calculator presents a 95% confidence interval. 6) (57.84, 60.48) x = Sx = 4.33 n = 45 Fill in the blanks: We are confident that the population mean is between and. A) 95%, 57.84, B) 5%, 0, C) 95%, 0, D) 5%, 57.84, ) The t-distribution has a variance that is greater than one. A) True B) False 7) 8) A researcher wants to construct a 99% confidence interval for the proportion of elementary school students in Seward County who receive free or reduced-price school lunches. What sample size is needed so that the confidence interval will have a margin of error of 0.07? A) 339 B) 277 C) 24 D) 10 8) 9) A college believes that 26% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points with 95% confidence? A) 296 B) 99 C) 444 D) 210 9) 10) The Pizza Shop wanted to determine what proportion of its customers ordered only cheese pizza. Out of 80 customers surveyed, 15 ordered only cheese pizza. What is the 99% confidence interval of the true proportion of customers who order only cheese pizza? A) < p < B) < p < C) < p < D) < p < ) 11) Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 11 pipes has a standard deviation of 10.6 inches. A) 54.9 < σ < B) < σ < C) 7.4 < σ < 18.6 D) 7.6 < σ < ) Page 2

3 12) Following are the heights in inches of 12 two-year-old apple trees. Assume that the population is normally distributed. 12) Construct a 99% confidence interval for the population standard deviation σ. A) 1.98 < σ < 5.63 B) 1.90 < σ < 6.09 C) 1.93 < σ < 5.86 D) 1.85 < σ < ) What is the value for χ 2 right for a 98% confidence interval when n = 12? 13) A) B) C) D) ) Are the following statements H 0 : = 12 and H 1 : 12 valid null and alternative hypotheses? A) Yes, these statements are two non-overlapping hypotheses and compare two parameters. B) No, there are no parameters contained in these statements. C) Yes, these statements are two non-overlapping hypotheses and compare a parameter to a value. D) No, the alternative hypothesis cannot contain numeric values. 15) A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 23.4 miles per gallon (mpg). A random sample of 56 cars are selected and the air filter of each is replaced with a new one. Let μ be the population mean fuel efficiency score that would occur if every car's air filter were replaced. The air filter change is deemed effective if μ > 23.4 mpg. A test is made of H 0 : μ = 23.4 versus H 1 : μ > ) 15) Assume that the air filter changes are not effective. Which type of error is impossible? A) Type II B) Type I 16) A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 24.3 miles per gallon (mpg). A random sample of 41 cars are selected and the air filter of each is replaced with a new one. Let μ be the population mean fuel efficiency score that would occur if every car's air filter were replaced. The air filter change is deemed effective if μ > 24.3 mpg. A test is made of H 0 : μ = 24.3 versus H 1 : μ > ) Assume that the air filter changes are effective but the conclusion is reached that the changes might not be effective. Which type of error, of any, has occurred? A) Mechanical failure B) No error - correct decision C) Type I D) Type II Page 3

4 17) Using the z table, determine the critical values for a two-tailed test when α = A) ±1.88 B) ±0.18 C) ±0.06 D) ± ) 18) What is the critical value for a two-tailed t test when α = 0.02 and n = 19? A) B) C) D) ) 19) At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 500 milliliters of water. The technician dispenses 49 samples of water and determines the volume of each sample. The 49 samples have a mean volume of x = ml. The machine is out of calibration if the mean volume differs from 500 ml. 19) The technician wants to perform a hypothesis test to determine whether the machine is ou of calibration. State the appropriate null and alternate hypotheses. A) H 0 : μ 501.2, H 1 : μ = B) H 0 : μ = 500, H 1 : μ 500 C) H 0 : μ = 500, H 1 : μ < 500 D) H 0 : μ = 501.2, H 1 : μ > ) A sample of 35 students enroll in a program that claims to improve scores on the quantitative reasoning portion of the Graduate Record Examination (GRE). The participants take a mock GRE test before the program begins and again at the end to measure their improvement. 20) The mean number of points improved was x = 20. Assume the standard deviation is σ = 64 and let μ be the population mean number of points improved. To determine whether the program is effective, a test is made of the hypotheses H 0 : μ = 0 versus H 1 : μ > 0. Do you reject H 0 at the α = 0.01 level? A) No B) Yes C) There is not enough information to draw a conclusion. 21) In a particular city, the average annual salary for secretaries is $28,000. A sample of 50 secretaries from Company A shows an average annual salary of $24,500 with a population standard deviation of $4500. Secretaries at Company A claim they are paid less than the city average. What is the test value for this claim? A) 0.78 B) 5.50 C) D) ) Page 4

5 22) According to Beautiful Bride magazine, the average age of a groom is now 26.2 years. A sample of 16 prospective grooms in Chicago revealed that their average age was 26.6 years with a standard deviation of 5.3 years. What is the test value for a t test of the claim? A) 0.59 B) 1.81 C) 0.30 D) ) 23) A scientist claims that only 65% of geese in his area fly south for the winter. He tags 65 random geese in the summer and finds that 20 of them do not fly south in the winter. If α = 0.05, is the scientist's belief warranted? A) Yes, because the test value is in the noncritical region. B) Yes, because the test value 0.72 is in the noncritical region. C) No, because the test value is in the noncritical region. D) No, because the test value 0.79 is in the critical region. 23) 24) In a simple random sample of size 100, there were 25 individuals in the category of interest. Compute the sample proportion p^. A) B) 125 C) D) ) 25) The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion p. 25) prop > 0.29 z = p = p^ = n = 73 State the null and alternate hypotheses. A) H 0 : p = 0.205, H 1 : p = 0.29 B) H 0 : p = 0.29, H 1 : p > 0.29 C) H 0 : p = , H 1 : p > D) H 0 : p = 0.205, H 1 : p > ) The Energy Information Administration reported that 51.5% of homes in the United States were heated by natural gas. A random sample of 200 homes found that 111 were heated by natural gas. Does the evidence support the claim or has the percentage changed? Use α = 0.05 and the P-value method. A) There is not enough information to draw a conclusion. B) No. There is enough evidence to reject the claim that the percentage of homes that are heated by natural gas is 51.5%. C) Yes. There is not enough evidence to reject the claim that the percentage of homes that are heated by natural gas is 51.5%. 26) Page 5

6 27) The χ 2 critical value for n = 16 and α = 0.01 for a left-tailed test is A) False B) True 27) 28) A machine fills 12-ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to 0.02 ounce. A sample of 8 bottles is selected, and the number of ounces of soda in each bottle is given. At α = 0.05, can you reject the claim that the machine is functioning properly? Justify your answer. (Assume that the variables are approximately normally distributed.) ) A) χ 2 = , χ 2 critical = ; There is evidence to reject the claim that the machine is working properly. B) χ 2 = , χ 2 critical = ; There is evidence to reject the claim that the machine is working properly. C) χ 2 = , χ 2 critical = ; There is evidence to reject the claim that the machine is working properly. D) χ 2 = , χ 2 critical = ; There is not enough evidence to reject the claim that the machine is working properly. 29) State the appropriate null and alternative hypothesis and find the critical values for a two-tailed test with α = 0.10 and n = 8. Use σ 2 = 196. A) H o: σ 2 = 196 B) H o: σ 2 = ) H 1: σ C. V. = 1.690, C) H o: σ 2 = 196 H 1: σ C. V. = 2.167, H 1: σ C. V. = 2.733, D) H o: σ 2 = 196 H 1: σ C. V. = 2.180, ) Consider the null hypothesis H 0 : μ 1 - μ 2 = 0. If the confidence interval for μ 1 - μ 2 does 30) not contain 0, the null hypothesis should be rejected. A) True B) False Page 6

7 31) A marketing firm asked a random set of married and single men how much they were willing to spend on a vacation. Is there sufficient evidence at α = 0.05 to conclude that is there a difference in the two amounts? 31) Married Men Single Men Sample size Sample mean $880 $825 Population variance A) No, because the test value 1.39 is outside the critical region < z < B) Yes, because the test value 3.95 is outside the critical region < z < C) Yes, because the test value 1.39 is inside the critical region < z < D) No, because the test value 0.28 is inside the critical region < z < ) A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. 32) Africa Asia X 1 = 63.3 yr. X 2 = 65.2 yr. σ 1 = 9.1 yr. σ 2 = 7.3 yr. n 1 = 120 n 2 = 150 What is an appropriate null hypothesis? A) H 0 : μ 1 > μ 2 B) H 0 : μ 1 = μ 2 C) H 0 : μ 1 μ 2 D) H 0 : μ 1 < μ 2 33) A test was made of H 0 : μ 1 = μ 2 versus H 1 : μ 1 < μ 2. The sample means were x 1 = 11 and 33) x 2 = 9, the sample standard deviations were s 1 = 7 and s 2 = 5, and the sample sizes were n 1 = 15 and n 2 = 13. Is H 0 rejected at the 0.05 level? (Hint: First compute the value of the test statistic.) A) No B) Yes Page 7

8 34) A amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down range.) She hits fourteen balls with driver A and 10 balls with driver B. The The drive distances (in yards) for the trials are show below. Driver A ) Driver B Assume that the populations are approximately normal. Can you conclude that there is a difference in the mean drive distances for the two drivers? Use the α = 0.01 level of significance. A) No B) Yes SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 35) Are low-fat diets or low-carb diets more effective for weight loss? A sample of 70 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 10.5 pounds with a sample standard deviation of 7.09 pounds. A second sample of 76 subjects went on a low-fat diet. Their sample mean weight loss was 18.0 with a standard deviation of Can you conclude that the mean weight loss differed between the two diets? Use the α = 0.05 level. 35) i). State the appropriate null and alternate hypotheses. ii). Compute the test statistic. iii). How many degrees of freedom are there, using the simple method? iv). Do you reject H 0? State a conclusion. Page 8

9 36) The number of calories in a 12-ounce serving of randomly-selected regular and lite beers is listed. Is there sufficient evidence to conclude that the mean number of calories for lite beers is significantly less than that for the regular beers? Use α = Assume the variables are approximately normally distributed. Regular: Lite: ) a.state the hypotheses. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 37) The football coach at State University wishes to determine if there is a change in offensive production between the first half and the second half of his team's recent games. The table below shows the first-half and second-half offensive production (measured in total yards gained per half) for the past six games. 37) Game First half yards Second half yards State the null and alternative hypotheses. A) H 0 : μd = 0, H 1 : μd = 16.3 B) H 0 : μd = 0, H 1 μd 0 C) H 0 : μd = 0, H 1 : μd > 0 D) H 0 : μd = 0, H 1 : μd < 0 Page 9

10 38) The football coach at State University wishes to determine if there is a decrease in offensive production between the first half and the second half of his team's recent games. The table below shows the first-half and second-half offensive production (measured in total yards gained per half) for the past six games. 38) Game First half yards Second half yards Compute the test statistic. A) B) C) D) ) A medical researcher is interested in whether patients' left arms or right arms are longer. If 9 patients participate in this study, how many degrees of freedom should the researcher use when finding the critical value for a t test? A) 9 B) 17 C) 16 D) 8 39) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 40) In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data were obtained: 40) Specimen A B Can you conclude that the mean weight differs between the two balances? i). State the null and alternative hypotheses. ii). Compute the test statistic. iii). State a conclusion using the α = 0.10 level of significance. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 41) Find p and q, if X 1 = 11, n 1 = 30, X 2 = 28, and n 2 = ) A) p = 0.64 and q = 0.36 B) p = 0.65 and q = 0.35 C) p = 0.36 and q = 0.64 D) p = 0.35 and q = 0.65 Page 10

11 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 42) Find p and q, if X 1 = 23, n 1 = 43, X 2 = 29, and n 2 = ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 43) 64% of students at a university live on campus. A random sample found that 28 of 45 male students and 39 of 50 of female students live on campus. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of male and female students who live on campus? A) No, because the test value is inside the noncritical region < z < B) Yes, because the test value is outside the noncritical region < z < C) Yes, because the test value is outside the noncritical region < z < D) No, because the test value is inside the noncritical region < z < ) 44) Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 42 at one school and 17 of 30 at the other have ear infections. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools? A) Yes, because the test value is outside the noncritical region < z < B) Yes, because the test value is outside the noncritical region < z < C) Yes, because the test value is outside the noncritical region < z < D) No, because the test value is inside the noncritical region < z < ) 45) In the F distribution, values of F cannot be negative, because variances are always positive or zero. A) False B) True 45) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 46) To determine whether two sample variances are equal, a researcher can use a(n). 46) Page 11

12 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 47) The bowling scores of a professional bowler during a two-day tournament are shown below. 47) Day Day Can you conclude that the variability of the scores is greater on the second day than on the first day? Use the α = 0.05 level of significance. A) Yes B) No 48) For the samples summarized below, test the hypothesis that the two variances are equal, atα = ) Sample 1 Sample 2 Sample variance Sample size 7 17 A) Reject the hypothesis because the test value 2.50 is less than the critical value B) Accept the hypothesis because the test value 6.25 is greater than the critical value C) Reject the hypothesis because the test value 6.25 is greater than the critical value D) Accept the hypothesis because the test value 2.50 is less than the critical value Page 12

13 Answer Key Testname: 1342_TEST 2_CHAPTERS 7-9_HCCS_REVIEW_2017 1) B 2) B 3) A 4) B 5) C 6) A 7) A 8) A 9) A 10) D 11) C 12) B 13) B 14) B 15) A 16) D 17) D 18) B 19) B 20) A 21) D 22) C 23) B 24) C 25) B 26) C 27) A 28) C 29) C 30) A 31) B 32) B 33) A 34) A 35) i). H 0 : μ 1 = μ 2 versus H 1 : μ 1 μ 2 ii) iii). 69 iv). Yes. There appears to be a difference in the mean 36) a. H 0 : μ lite = μ regular ; H 1 : μ lite < μ regular b. t crit = c. t = d. reject e. There is evidence to conclude that the lite beer 37) B 38) A 39) D Page 13 40) i). H 0 : μd = 0, H 1 : μd 0 41) D ii) iii). Reject H0. The mean difference appears to differ 42) p = = and q = = ) D 44) D 45) B 46) F test 47) A 48) D