Math 1342 ExaM 3 ChaptErs NaME

Transcription

1 Math 1342 ExaM 3 ChaptErs NaME DatE ) 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 ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 2) If the correlation coefficient r is equal to 0.652, find the coefficient of nondetermination. A) B) C) D) ) 1

2 3) 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 6 subjects. Times were measured in thousandths of a second. The results are presented in the following table. 3) The following MINITAB output describes the fit of a linear model to these data. Assume that the assumptions of the linear model are satisfied. The regression equation is Auditory = Visual Predictor Constant Visual Coef SE Coef T P What is the slope of the least-squares regression line? A) B) C) D) ) Find the equation of the regression line. x y ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 5) If the correlation coefficient r is equal to 0.566, find the coefficient of determination. A) B) C) D) ) 6) Compute the standard error of the estimate for the data below. X values Y values A) 4.26 B) 7.47 C) 2.76 D) ) 2

3 7) Daniel Wiseman, a scientist for Gres-Trans Corp., wants to determine if the flow rate of a particular material changes with different changes in temperature. The data is plotted in the figure below. What type of relationship exists between the flow rate and the change in temperature? 7) A) There is no relationship. B) curvilinear C) positive D) negative 8) A multiple regression line was calculated in which x 1 was a student's grade point average and x 2 was a student's age. The multiple regression line was calculated as y = x x 2. If a student has a grade point average of 5.9 and is 20 years old, what is the predicted value of y? A) B) C) D) ) 9) A correlation coefficient r was calculated to be The coefficient of determination would be approximately. 9) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) For a prediction value of y from a specific value x, which of the following contribute to the prediction error? A) The error in estimating the intercept B) The standard error of the estimate C) The error in estimating the slope D) All of the above 10) 11) Compute the value of the correlation coefficient. x y A) B) C) D) ) 12) A regression line can be used to show trends in data. A) False B) True 12) 3

4 13) The total blood cholesterol concentrations, in mg/dl, are shown below for a random sample of six people. In the table below, x is the age of the subject and y is the subject's total cholesterol concentration. Find the 95% prediction interval when x = 58 years. 13) x (age) y (mg/dl) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 14) Frequencies obtained by calculation are called expected frequencies. A) True B) False 14) 15) A quality control supervisor selected a sample of 100 electronic components from each of three different production chains to determine if the production chains had the same rates of meeting their quality standards. At α = 0.05, test the claim that the proportions are equal. Components Chain 1 Chain 2 Chain 3 Meets the standard Does not meet the standard Total A) There is evidence to reject the claim that the proportions are equal because the test value > B) There is not evidence to reject the claim that the proportions are equal because the test value > C) There is not evidence to reject the claim that the proportions are equal because the test value < D) There is evidence to reject the claim that the proportions are equal because the test value < ) 4

5 16) A random group of seniors was selected from a university and asked about their plans for the following year. The school advising office claims that 50% of the students plan to work, 20% of the students plan to continue in school, and 30% of the students plan to take some time off. Is there evidence to reject this hypothesis at α = 0.05? Plans Work School Time off Number of students A) There is not evidence to reject the claim that the students' plans are distributed as claimed because the test value < B) There is evidence to reject the claim that the students' plans are distributed as claimed because the test value < C) There is not evidence to reject the claim that the students' plans are distributed as claimed because the test value < D) There is evidence to reject the claim that the students' plans are distributed as claimed because the test value < ) In a chi-square goodness-of-fit test when there is close agreement between the observed frequency and the expected frequency, the chi-square test value will be small. A) False B) True 16) 17) 18) The number of visits to a certain web site were counted each day of a particular week. The results are given in the following table. 18) Day Number of Visits Sunday 140 Monday 121 Tuesday 113 Wednesday 110 Thursday 130 Friday 134 Saturday 140 Test the hypothesis that the web site visits are equally likely to occur on any day of the week. Use the α = 0.01 level of significance. 5

6 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 19) A random group of desktop computer sales was selected from an electronic discount chain to analyze the size of monitor purchased with the computer. Is there evidence to reject the hypothesis that the number of monitors is equally distributed between the five types, atα = 0.05? Monitor type 15" CRT 15" flat panel 17" CRT 17" flat panel 19" CR Number of sales A) There is not evidence to reject the claim that the monitors are equally distributed between the five classes because the test value < B) There is evidence to reject the claim that the monitors are equally distributed between the five classes because the test value > C) There is not evidence to reject the claim that the monitors are equally distributed between the five classes because the test value < D) There is evidence to reject the claim that the monitors are equally distributed between the five classes because the test value > ) 20) The degrees of freedom for a 3 5 contingency table are. 20) 21) A sample of 141 university students who recently moved off-campus were polled to see whether they agree that off-campus living is preferable to on-campus living. In addition, each was asked how many people live in their current off-campus residence. The results are summarized in the following contingency table. 21) Agree No Opinion Disagree i). Compute the row totals, the column totals, and the grand total. ii). Construct the corresponding table of expected values. iii). Compute the value of the chi-square test statistic. iv). Perform a test for independence, using the α = 0.05 level of significance. What do you conclude? 6

7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 22) A sociologist wanted to determine whether there was a difference in the amount of time children aged 5 7 spent watching television each day. Check the following data for evidence that the number of minutes spent watching television is equally distributed throughout the week. Use α = ) Day Number of Minutes Sunday 200 Monday 112 Tuesday 123 Wednesday 130 Thursday 160 Friday 225 Saturday 247 Compute the test value. A) B) 100 C) D) ) A sociologist wanted to determine whether there was a difference in the amount of time children aged 5 7 spent watching television each day. Check the following data for evidence that the number of minutes spent watching television is equally distributed throughout the week. Use α = ) Day Number of Minutes Sunday 200 Monday 112 Tuesday 123 Wednesday 130 Thursday 160 Friday 225 Saturday 247 Find the critical value. A) B) C) D)

8 24) The table lists the number of students from three different high schools participating in the mathematics and physics sections of a science fair. At α = 0.05, test the claim that the section of participation and the high school where the students were from are independent. Number of Students High School 1 High School 2 High School 3 Mathematics Physics A) There is evidence to reject the claim that the high school and the section of participation are independent because the test value > B) There is evidence to reject the claim that the high school and the section of participation are independent because the test value > C) There is evidence to reject the claim that the high school and the section of participation are independent because the test value > D) There is not evidence to reject the claim that the high school and the section of participation are independent because the test value < ) 25) Two computer stores recorded the number of computers sold in a week along with the sizes of their hard drives. At α = 0.05, test the claim that the distribution of hard drives and the store where the computers were bought are not related. Number of computers 20 GB drive 40 GB drive 80 GB drive 160 GB drive Store Store A) There is not evidence to reject the claim that the size of hard drive sold and the store number are not related because the test value < B) There is evidence to reject the claim that the size of hard drive sold and the store number are not related because the test value > C) There is evidence to reject the claim that the size of hard drive sold and the store number are not related because the test value > D) There is evidence to reject the claim that the size of hard drive sold and the store number are not related because the test value > ) 8

9 26) A biologist had mice and rats run through a maze and recorded the number that finished the maze successfully and the number that did not. The table lists the results of the study. Atα = 0.05, test the claim that the rodent type and the success of finishing the maze are not related. Mice Rats Finished Did not Finish A) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value > B) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value < C) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value < D) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value > ) 27) A researcher is comparing 4 groups to test if they have the same means. There are 64 data values altogether. The degrees of freedom for the Between (dfb) and the degrees of freedom for the Within (dfw) are A) dfb = 4, dfw = 63 B) dfb = 3, dfw = 63 C) dfb = 60, dfw = 63 D) dfb = 3, dfw = 60 27) 28) If there is no difference in the means, the variance will be approximately equal to the within-group variance. 28) 29) When there is one independent variable, the analysis of variance is called a ANOVA. 29) 9

10 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 30) A Two-Way ANOVA Summary Table is shown below. 30) Source SS d.f. MS F Factor A Factor B Interaction A B Within (error) Total The critical value for the F-test using α = 0.05, d.f.n. = 2, and d.f.d = 54 is Then, A) The null hypothesis concerning Factor A should be rejected B) The null hypothesis concerning Factor A and the Interaction (A B) effect should be rejected C) The null hypothesis concerning Factor B should be rejected D) All of the null hypotheses should be accepted 31) A portion of an ANOVA summary table is shown below. Calculate the F-test value. 31) Source Sum of Squares Degrees of Freedom Between 16 2 Within (error) Total 59 A) 5.77 B) C) 0.17 D) ) The F-test for comparing means is always right tailed. A) False B) True 32) 10

11 33) An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together end-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond apart. For each combination of curing time and curing temperature, three tests are performed. The results of the experiment are shown below. 33) Low cure temp High cure temp 1-hr cure time 2-hr cure time 3-hr cure time Can the main effect of curing time on bonding strength be interpreted? If so, interpret the main effect. using the α = 0.01 level of significance. A) Yes. Reject H 0. B) Yes. Do not reject H 0. C) No. 34) Which of the following assumptions does not apply to the two-way ANOVA? A) The means of the populations must be equal. B) The samples must be independent of each other. C) The groups must be equal in sample size. D) The populations from which the samples were obtained must be normally or approximately normally distributed. 34) 35) Independent variables can also be called. 35) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 36) Complete the formula for the sum of squares between groups: s B 2 = 36) A) (X i - X j ) 2 s 2 w (1/n i + 1/n j ) B) n i (X i - X GM ) 2 k - 1 C) (n i - 1) s 2 i (n i - 1) D) X i - X j s 2 w /n 11

12 37) If there are 6 means to be compared, then how many possible different comparisons (such as X 2 compared to X 3 ) are there altogether? A) 30 B) 6 C) 15 D) 36 37) 38) The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubber content. 38) Low Rubber Medium Rubber High Rubber Low Binder Content Medium Binder Content High Binder Content Content Content Content Can you reject the hypothesis of no interactions? A) Yes B) No 39) A vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of coffee. Their data is given below. 39) Machine A Machine B Machine C Compute the test value for the coffee machines. A) 2.25 B) 5.06 C) 4.86 D)