2.57 when the critical value is 1.96, what decision should be made?

Transcription

1 Math 1342 Ch Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question ) If the test value for the difference between the means of two large samples is 2.57 when the critical value is 1.96, what decision should be made? 1) 2) A bond analyst is analyzing the interest rates for equivalent municipal bonds issued by two different states. At α = 0.05, is there enough evidence to conclude that there is a difference in the interest rates paid by the two states? State A State B Sample size Mean interest rate (%) Population variance ) An educational researcher is analyzing the test scores for physics students taught using two different methods - a traditional method, and a web-based self-paced method. Can he conclude, at α =.05, that the test scores in the web-based self-paced method are lower? 2) 3) Traditional Web-based Self-paced Sample size Mean test score Population variance ) 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. 4) 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 Calculate the critical value. Use α =

2 5) The average credit card debt for a recent year was $8824. Five years earlier the average credit card debt was $8159. Assume sample sizes of 35 were used and the population standard deviations of both samples were $1396. Is there evidence to conclude that the average credit card debt has increased? Use α = ) a. State the hypotheses. b. Find the critical value. c. Compute the test statistic. d. Make the decision. e. Summarize the results ) A test was made of H 0 = μ 2 versus H 1 < μ 2. The sample means were 6) x 1 = 13 and x 2 = 12, the sample standard deviations were s 1 = 4 and s 2 = 3, and the sample sizes were n 1 = 16 and n 2 = 15. How many degrees of freedom are there for the test statistic? 7) A test was made of H 0 = μ 2 versus H 1 < μ 2. The sample means were 7) x 1 = 11 and 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.) 8) 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. 2

3 9) A garden seed wholesaler wishes to test the claim that tomato seeds germinate faster when each individual seed is "pelletized" within a coating of corn starch. The table below shows the germination times, in days, of six pelletized seeds. The table also shows the germination times in days of six un-coated seeds (the controls). 9) Pelletized: Control: Can you conclude that the mean germination time for pelletized seeds is less than the mean for the un-pelletized seeds? Use the α = 0.05 level of significance. 10) In a test of the difference between the two means below, what should the test value be for a t test? 10) Sample 1 Sample 2 Sample mean Sample variance Sample size ) Twelve dieters lost an average of 12 pounds in 6 weeks when given a special diet plus a "fat-blocking" herbal formula. A control group of twelve other dieters were given the same diet, but without the herbal formula, and lost an average of 8.2 pounds during the same time. The standard deviation of the "fat-blocker" sample was 2.8 and the standard deviation of the control group was 2.6. Find the 95% confidence interval for the differences of the means. 12) Twelve dieters lost an average of 5.2 pounds in 6 weeks when given a special diet plus a "fat-blocking" herbal formula. A control group of twelve other dieters were given the same diet, but without the herbal formula, and lost an average of 4.5 pounds during the same time. The standard deviation of the "fat-blocker" sample was 2.8 and the standard deviation of the control group was 2.5. Find the 95% confidence interval for the differences of the means. 11) 12) 3

4 13) Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtained the data shown in the table below. 13) Imported Wine Domestic Wine X 1 = $7.03 X 2 = $9.78 s 1 = $2.31 s 2 = $3.62 n = 15 n = 16 What is the critical value at α = 0.05? 14) A marketing firm asked a random set of married women and married men how much they were willing to spend for jewelry as a present for their spouse. Can the firm conclude, atα = 0.05, that the two groups have a different willingness to spend? 14) Women Men Sample size 9 16 Sample mean $160 $205 Sample standard deviation $34 $ ) Following is a sample of five matched pairs. 15) Sample Sample Let μ 1 and μ 2 represent the population means and let μ d = μ 1 μ 2. A test will be made of the hypotheses H 0 : μ d = 0 versus H 1 : μ d > 0. Compute the test statistic. 4

5 16) 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: 16) 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. 17) 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. 17) Game First half yards Second half yards Can you conclude that the mean offensive production in the first half differed from that of the second half? i). State the null and alternative hypotheses. ii). Compute the test statistic. iii). State a conclusion using the α = 0.02 level of significance. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question ) Samples are independent when they are not related. A) True B) False 18) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 19) The critical value for a left-tailed t test for dependent samples is when there are seven degrees of freedom and α = ) 5

6 20) Find p and q, if X 1 = 11, n 1 = 30, X 2 = 28, and n 2 = ) 21) A poll found that 39% of male voters and 42% of female voters support a particular candidate. To test whether this candidate has equal levels of support between male and female voters, the alternative hypothesis should be 22) 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? 23) A recent survey reported that in a sample of 300 students who attend two-year colleges, 105 work at least 20 hours per week. Additionally, in a sample of 225 students attending private four-year universities, only 20 students work at least 20 hours per week. What is the test value for a test of the difference between these two population proportions? 24) 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? 21) 22) 23) 24) ) The two variables in a scatter plot are called the 25) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 26) The range of the correlation coefficient is from 0 to 1. A) False B) True 26) 27) Ten pairs of points yielded a correlation coefficient r of If α = 0.05, which of the following statements is correct if H 0 : ρ = 0? (Do not calculate a t-value.) A) There is no correlation between the variables. B) Because is greater than 0.632, the null hypothesis is rejected. C) Because is greater than 0.632, the null hypothesis is not rejected. D) Because is greater than 0.602, the null hypothesis is not rejected. 27) 6

7 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 28) A study was conducted to determine if there was a linear relationship between a person's age and his/her peak heart rate. a. Draw the scatter plot for the variables. b. Give a brief explanation of the type of relationship. Age Peak Heart Rate ) Compute the value of the correlation coefficient. x y ) 29) ) Test the significance of the correlation coefficient r at α = 0.05 for the data below. 30) X values Y values ) A study was conducted to determine if there was a relationship between the prices a non-member of a book club paid for various publications and the prices that a member paid for the same publications. The data gathered is shown below. Compute the value of the correlation coefficient. Non-member Member Price Price ) When r is not significantly different from 0, the best predictor of y is the of the data values of y. 31) 32) 7

8 33) The equation of a regression line is y = x. What is the intercept of this line? 34) What is the value of y when x = 3, if the equation of the regression line is y = x? 35) Find the equation of the regression line. x y ) 34) 35) 36) In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths of a second. The results are presented in the following table. 36) Visual Auditory Compute the least-squares regression line for predicting auditory response time (y from visual response time (x) ) If the correlation coefficient is 0.790, what is the explained variation? 37) 38) If the correlation coefficient is 0.930, what is the unexplained variation? 38) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 39) A correlation coefficient r was calculated to be The coefficient of nondetermination would be A) True B) False 39) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 40) If the correlation coefficient r is equal to 0.566, find the coefficient of determination. 40) 8

9 41) If the correlation coefficient r is equal to 0.547, find the coefficient of determination and the coefficient of nondetermination. 42) Compute the standard error of the estimate for the data below. Round to the thousandths place. 41) 42) x y ) Compute the standard error of the estimate for the data below. X values Y values ) 9

10 Answer Key Testname: MATH 1342 CH REVIEW 1) Reject the null hypothesis. 2) Yes, because the test value is outside the critical region < z < ) The data supports the claim because the test value 3.30 is greater than the critical value ) ) a. H 0 = μ 2 ; H 1 < μ 2 b. C.V. = 1.65 c. z = 1.99 d. reject e. There is evidence to conclude that the average credit card debt has increased. 6) 14 7) No 8) 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 beers contain fewer calories. 9) Yes 10) ) 1.4 < μ 1 - μ 2 < ) -1.7 < μ 1 - μ 2 < ) ) Yes, because the test value is outside the noncritical region < t < ) ) i). H 0 : μd = 0, H 1 : μd 0 ii) iii). Reject H 0. The mean difference appears to differ from zero. 17) i). H 0 : μ d = 0, H 1 : μ d > 0 ii) iii). Reject H 0. The mean offensive production appears to decrease from the first half to the second half. 18) A 19) ) p = 0.35 and q = ) H 1 : P male P female. 22) No, because the test value is inside the noncritical region < z < ) ) No, because the test value is inside the noncritical region < z < ) independent variable and dependent variable. 26) A 27) B 10

11 Answer Key Testname: MATH 1342 CH REVIEW 28) a. b. There appears to be a negative relationship between age and peak heart rate. 29) ) Reject ρ = 0 because > ) ) mean 33) ) ) y = 2.186x ) y = x 37) 62.4% 38) 13.5% 39) B 40) ) The coefficient of determination is and the coefficient of nondetermination is ) )