 # General Statistics Questions

## Transcribed Text

1) The statistical model used to conduct the data analysis in this paper was a)Simple linear regression b)One way analysis of variance c)Multiple linear regression d)Two way analysis of variance e)Contingency table 2)The independent variable in the statistical model used in this paper was a)Method of payment used to purchase gasoline b)Number of gallons of gasoline purchased c)Type of vehicle driven d)Time to complete gasoline purchase 3)The dependent variable in the statistical model used in this paper was a)Method of payment used to purchase gasoline b)Number of gallons of gasoline purchased c)Type of vehicle driven d)Time to complete gasoline purchase 4)Which of the following best explains a Pearson correlation coefficient equal to zero forvariables X and Y? a)There is perfect linear association between X and Y b)There is no association between X and Y c)There is no linear association between X and Y d)Values of X minus the values of Y always equal zero 5)The following one way analysis of variance hypothesis was rejected at the 5% level ofsignificance: Ho: μ1 = μ2 = μ3 = μ4 H1: at least one mean differs Under the Tukey method for post-hoc analysis, how many pair-wise comparisons of means must be conducted? a)4 b)5 c)6 d)8 e)10 6)One way analysis of variance is an extension of which of the following statistical tests? a)Dependent t test b)Confidence interval for the standard deviation c)Matched pairs test d)Independent t test of two means e)Confidence interval for the proportion 7)The Pearson correlation coefficient for X and Y equals 0.9552. Which of the following is thecorrect interpretation of this result? a)Values of X cause values of Y b)Values of Y cause values of X c)Small values of X tend to be found with small values of Y; large values of X tend to be foundwith large values of Y. d)Large values of X tend to be found with small values of Y; small values of X tend to be foundwith large values of Y. Use this information to answer Questions 8, 9, 10, 11 and 12 which appear on the next page A marketing analyst is investigating the impact of advertising expenditures X (measured in \$000,000) on the sales of a product Y (measured in thousands of units sold, 000). After running a successful correlation analysis the analyst then fit a statistically significant regression model at the 5% level of significance. The JMP output for the regression analysis and summary statistics for X and Y is shown below. Summary Statistics for Y: Summary Statistics for X: 8)Which of the following best describes the strength of this regression model? a)22.16 percent of the variation in Sales is explained by the regression with Advertising b)95.00 percent of the variation in Sales is explained by the regression with Advertising c)5.00 percent of the variation in Sales is explained by the regression with Advertising d)75.21 percent of the variation in Sales is explained by the regression with Advertising e)77.96 percent of the variation in Sales is explained by the regression with Advertising 9)For a \$100,000 increase in advertising expenditures sales is expected to increase by ______units. a)219 b)2194 c)1488 d)2830 10)What is the relevant range of values (in \$000,000) of advertising expenditures for makingpredictions of sales using this regression model? a)2.8 ≤ X ≤ 4.0 b)X ≥ 9.5 c)X ≥ 10.0 d)6.0 ≤ X ≤ 11.0 11)The value of the Pearson r correlation coefficient for this regression was a)0.470833 b)0.867224 c)0.882964 d)0.393148 e)0.445222 12)The form of a 95% confidence interval for a predicted value of sales units (Y) for a givenvalue of advertising expenditure (X) is: 𝑌̂−(𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟)(𝑆𝑒)≤𝑌≤ 𝑌̂+(𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟)(𝑆𝑒) To compute this interval for the problem under study, what value would be used for the standard error Se? a)1.7919573 b)0.049140 c)0.221684 d)0.373642 e)0.041237 Use the information below to answer Questions 13 and 14 which appear on the next page A market researcher conducted a study of 291 randomly selected Web sites used for on line shopping that that were headquartered in France, UK and USA. The researcher was interested in studying the location of the privacy disclaimer statement as a measure of the degree of personal protection of shopper information. The privacy disclaimer to the shopper using the Web site to make a purchase appeared on either the Home Page, the Order Page, the Client Page or some Other Page. The data are in the table below; a JMP output for a Chi Square Analysis of this data is also below. Location of Disclaimer: Home Page Order Page Client Page Other Page Nationality of Web Site FranceUKUSA Total 56 68 35 159 19 19 28 66 6 10 16 32 12 9 13 34 Total 93 106 92 291 13)Given that the nationality of the web site was USA, what percentage of the privacydisclaimers where found on the client page? a)5.5% b)31.6% c)50.0% d)17.4% e)88.1% 14)The researcher is interested in testing the following hypothesis: Ho: The location of the privacy disclaimer is independent of the nationality of the web site H1: The location of the privacy disclaimer is dependent on the nationality of the web site At the 5% level of significance, what is the researcher’s decision? a)At the 5% level of significance reject the null b)At the 5% level of significance fail to reject the null c)At the 5% level of significance the test is inconclusive and no decision can be made The Pearson correlation matrix for four variables is given below. Use this information to answer questions 15 and 16. CORRELATIONS 15)Which pair of variables has the strongest linear association? a)Q and W b)S and W c)S and Q d)X and Q 16)Which pair of variables has the weakest linear association? a)Q and W b)S and Q c)S and W d)X and W 17)The least squares procedure for linear regression models results in estimators for modelfitting which are BLUE (Best Linear Unbiased Estimators). Which of the following correctlydescribes the statistical characteristics of BLUE estimators in linear regression? a)The BLUE estimators are unbiased and maximum variance b)The BLUE estimators are unbiased and minimum variance c)The BLUE estimators are unbiased and zero variance Use this information to answer questions 18, 19 and 20. In a study of the cost of bumper damage caused by a head on impact for a specific make of automobile, a researcher examined the dollar value of bumper damage incurred for three types of bumpers and for four impact speeds using two factor analysis of variance. The bumpers were made out of three different types of alloy: alloy A, alloy B and alloy C. The four different impact speeds were 5 mph, 10 mph, 15 mph and 20 mph. Three automobiles were tested for each treatment combination of bumper type and impact speed using a robotic controlled crash of the automobiles into a concrete retaining wall. The damaged bumpers were then inspected by an automobile repair expert who assigned a dollar value to the degree of damage that the bumper received as a result of the impact. 18)How many treatment combinations were there in this study? a)2 b)3 c)8 d)12 e)36 19)If the null hypothesis of no interaction between type of bumper and impact speed is rejectedat the 5% level of significance, what should be the researcher’s next step in the analysis? a)Test the main effect of bumper type and the main effect of impact speed using individual Ftests for each b)Perform a post-hoc analysis on the bumper type and impact speed interaction c)Stop the study and conclude that there is no effect on the dollar value of bumper damage as aresult of bumper type and impact speed. 20)Which factor had the most levels? a)Bumper type b)Impact speed c)Both factors had an equal number of levels

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1(B)
2(A)
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