math 214 (multivariable statistics)lycofs01.lycoming.edu/~sprgene/m214/class2014/multi… · web...

MATH 214 Class Handout #4 1

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11. Read Part 1 of the “PRACTICAL EXERCISES” section at the end ofChapter 1. You should find that four separate analyses are to be done. Also, you should find that there are seven answers required for each analysis. Assume that the significance level is 0.05 for each hypothesis test.

(a) Of the four separate analyses to be done, identify the one where a Pearson or Spearman correlation could be used.

(b) Answer #1, and also indicate whether the hypothesis test should be one-sided or two-sided.

(c) Answer #2.

(d) Answer #3 and #4.


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(e) Answer #5 by using SPSS to do the appropriate calculations and to create an appropriate graphical display; attach the SPSS output to this assignment. At the top of the printout, write a title in the following format:

Your Name - Math 214(your section) - Today's DateClass Handout #4 Homework - Exercise #11Textbook Chapter 1

(f) Answer #6 by writing a paragraph patterned after the one used to answer Exercise #1 on this Class Handout #4 (which includes the results for the parametric analysis and for the nonparametric analysis).

(Note: you do not have to answer #7 for this analysis, since a table would be used only when many correlations need to be displayed simultaneously.)



(a) Of the four separate analyses to be done, identify the one where an independent samples t test or a Mann-Whitney rank sum test could be used.


(c) Answer #2.



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(e) Answer #5 by using SPSS to do the appropriate calculations and to create an appropriate graphical display; attach the SPSS output to this assignment. At the top of the printout, write a title in the following format:


(f) Answer #6 by writing one paragraph summarizing the results of Levene’s test and what these results imply about the parametric analysis, one paragraph summarizing the results of the appropriate parametric analysis, and one paragraph summarizing the results of the nonparametric analysis. Pattern each paragraph after the summaries of results in Exercises #3 and #4 on this Class Handout #4.

(Note: you do not have to answer #7 for this analysis, since a table would be used only when many more analyses need to be displayed simultaneously.)


13. Read Part 2 of the “PRACTICAL EXERCISES” section at the end ofChapter 1. You should find that there are seven answers required for the desired analysis. Assume that the significance level is 0.05 for each hypothesis test.

(a) Explain why a dependent samples t test or a Wilcoxon signed rank test could be used in this analysis.


(c) Answer #2.



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(e) Answer #5 by creating the required SPSS data file, saving the data file with an appropriate name in your personal folder on the college network, using SPSS to do the appropriate calculations and to create an appropriate graphical display, and attaching the SPSS output to this assignment. At the top of the printout, write a title in the following format:


(f) Answer #6 by writing by writing one paragraph summarizing the results of the appropriate parametric analysis and one paragraph summarizing the results of the nonparametric analysis. Pattern each paragraph after the summaries of results in Exercises #5 and #6 on this Class Handout #4.



14. The mean length of fish is being studied for North Lake, Blue Lake, andHarvey Lake. A 0.01 significance level is chosen for a hypothesis test to see if there is any evidence that mean length of fish is not the same for the three lakes. Fish are randomly selected from each lake, and the lengths in inches are recorded as follows:

North 13 17 15 18 17

Blue 15 12 16 11 16

Harvey 14 10 12 13 11

(a) Find the sample means, and then complete the following ANOVA table:

Source df SS MS f P-value

Error

Total

(b) Summarize the results (Step 4) of the f test to see if there is sufficient evidence that mean length of fish is not the same for the for the three lakes at the 0.01 level. State whether or not any further analysis is needed, and explain why or why not. (If further analysis is needed, you do not have to do it.)


15. The mean breaking strength for each of three types of rope (named Deluxe,Econ, and Nogood) is being studied. A hypothesis test will be performed to see if there is any evidence that mean breaking strength is not the same for the rope types. A 0.10 significance level is chosen for all hypothesis testing. Pieces of rope are randomly selected from each type, and the breaking strengths in pounds of force are recorded as follows:

Deluxe 165 162 159 162

Econ 156 163 158

Nogood 151 154 160

(a) Use SPSS to perform the necessary calculations for this hypothesis test and to create an appropriate graphical display, by doing the following:

Step 1:Create an SPSS data file named rope containing two variables named type and strength (and save this data file in your personal folder on the college network). Define codes for the variable type so that 1 (one) represents the rope type Deluxe, 2 (two) represents the rope type Econ, and 3 (three) represents the rope type Nogood. Store the data in this SPSS file by entering each breaking strength together with the corresponding coded value for each of the rope types.

Step 2:With this data and the appropriate guidelines in the document titled Using SPSS Version 19.0, use SPSS to do the necessary calculations and to create an appropriate graphical display, making certain to have descriptive statistics displayed, to have the results of Levene’s test displayed, and to have the results of Tukey’s HSD multiple comparison method displayed; it will not be necessary to display the results of either of the alternative f tests which are adjusted for unequal variances.


http://www.lycoming.edu/~sprgene/SPSSWIN.html


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Step 3:Double click on the title Oneway in the SPSS output, and edit the title so that it is in the following format:

One-Way ANOVA for Mean Breaking Strengthwith Three Rope TypesExercise #15(a) of Class Handout #4Your Name – Today’s Date - Math 214

When you are finished editing the title, click once in a blank area to leave the title editor.

Step 4:Double click on the title Explore in the SPSS output, and edit the title so that it is in the following format:

Box Plots of Breaking Strength with Three Rope TypesExercise #15(a) of Class Handout #4Your Name – Today’s Date - Math 214


Step 5:Make certain that no item in the output is selected. (If any item is selected, click once in a blank area to deselect the item.) From the main menu of the SPSS output window, use the File > Print Preview options to see what the printout will look like. If you notice any table that has been divided because it will not fit across the page, then you should format your output to print in Landscape. If any title needs to be moved to the top of the next page, click on the Close button to leave the print preview, click once on the title to select it, and select the Insert> Page Break options. Use the File > Print Preview options again to check the output, until you are satisfied with the way the output will be printed.

Step 6:Exit from SPSS. Submit the printed output as part of this homework assignment.


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(b) Making use of the SPSS output from part (a), first write a brief paragraph to summarize the results (Step 4) of Levene’s test and indicate what these results say about the appropriateness of the f test in the one-way ANOVA. Next, in a second paragraph, summarize the results (Step 4) of the f test in the one-way ANOVA. Finally, if multiple comparison is necessary, make use of the SPSS output from part (a) to summarize the results of Tukey’s HSD multiple comparison method in a third paragraph; if no further analysis is needed, explain why not. (Recall that a 0.10 significance level is chosen for all hypothesis testing.)


16. Consider data for a one-way ANOVA where each of three treatments,labeled A, B, and C, are applied to 4 subjects (that is, the data will consist of 3 random samples each of size 4).

(a) Make up a data set for which the between groups sum of squares will be 0 (zero), but the within groups sum of squares will not be 0 (zero). (Hint: This means you need a data set for which there is no variation between samples but there is some variation within samples.)

A

B

C

(b) Make up a data set for which the within groups sum of squares will be 0 (zero), but the between groups sum of squares will not be 0 (zero). (Hint: This means you need a data set for which there is no variation within samples but there is some variation between samples.)

A

B

C


17. Read Part 1 of the “PRACTICAL EXERCISES” section at the end of Chapter 1. You should find that four separate analyses are to be done. Also, you should find that there are seven answers required for each analysis. Assume that the significance level is 0.05 for each hypothesis test.

(a) Of the four separate analyses to be done, identify the one where a one-way ANOVA together with a Bonferroni multiple comparison (if necessary) could be used, or a Kruskal-Wallis test together with a Tamhane’s T2 multiple comparison (if necessary) could be used.

(b) Answer #1, and also indicate whether the hypothesis test should be one sided or two sided.

(c) Answer #2.



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(e) Answer #5 by using SPSS to do the appropriate calculations and to create an appropriate graphical display; attach the SPSS output to this assignment; make certain to include output for descriptive statistics, for Levene’s test, and for the parametric and nonparametric tests with corresponding multiple comparison procedures mentioned in part (a). At the top of the printout, write a title in the following format:


(f) Answer #6 by writing one paragraph summarizing the results of Levene’s test and what these results imply about the parametric analysis, one paragraph summarizing the results of the appropriate parametric analysis, and one paragraph summarizing the results of the nonparametric analysis. Pattern each paragraph after the summaries of results in Exercises #7 and #8 on Class Handout #4.


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18. Randomly selected customers of a car dealership are polled in order tocollect data concerning area of residence and preferred color of a certain type of sports car. For each customer, an area of residence is recorded as rural, suburban, or urban, and color preference is recorded chosen from red, green, yellow, and white. The data are stored in the SPSS data file sportscar.

(a) If there were an association between area of residence and preferred color of the sports car, then describe what could be said about how the distribution of proportions preferring the different colors would compare among the various areas of residence.

(b) The data are to be used to perform a hypothesis test to see if there is any evidence of an association between area of residence and preferred color of the sports car. A 0.05 significance level is chosen. Use SPSS to perform the necessary calculations for this hypothesis test and to create an appropriate graphical display, by doing the following:

Step 1:With the data file sportscar, where each line of the data file represents one case, and with the appropriate guidelines in the document titled Using SPSS Version 19.0, use SPSS to do the necessary calculations and to create an appropriate graphical display, making certain that the rows and columns of the contingency table displayed in SPSS respectively represent the variables area of residence and color preference; also make certain that the SPSS output displays the data (observed frequencies), the expected frequencies, the percentages for color preferences among area of residence, and the standardized residuals for each cell.




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Step 2:Double click on the title Crosstabs in the SPSS output, and edit the title so that it is in the following format:

Chi-Square Test for Association BetweenCar Color Preference and Area of ResidenceExercise #18(b) of Class Handout #4Your Name – Today’s Date - Math 214


Step 3:Double click on the title Graph in the SPSS output, and edit the title so that it is in the following format:

Stacked Bar Chart for Distribution ofCar Color Preferences Among Areas of ResidenceExercise #18(b) of Class Handout #4Your Name – Today’s Date - Math 214


Step 4:Make certain that no item in the output is selected. (If any item is selected, click once in a blank area to deselect the item.) From the main menu of the SPSS output window, use the File > Print Preview options to see what the printout will look like. If you notice any table that has been divided because it will not fit across the page, then you should format your output to print in Landscape. If any title needs to be moved to the top of the next page, click on the Close button to leave the print preview, click once on the title to select it, and select the Insert> Page Break options. Use the File > Print Preview options again to check the output, until you are satisfied with the way the output will be printed.

Step 5:Exit from SPSS. Submit the printed output as part of this homework assignment.


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(c) Explain how we know that the sample size with the given data is sufficiently large for the chi-square hypothesis test in part (b) to be appropriate.

(d) Summarize the results (Step 4) of the hypothesis test in part (b) to see if there is any evidence of an association between area of residence and preferred color of the sports car, with = 0.05. Then, indicate whether or not it is necessary to describe the relationship, and say why or why not. If necessary, use the standardized residuals to describe the relationship.


19. A random sample of individuals are polled in order to collect dataconcerning customer preference for cable and satellite television channels in various geographic areas. The following contingency table is constructed from this data:

Channel PreferenceResidence Cartoon Comedy Sci Fi Western

Rural 28 7 17 53 105Suburban 22 34 36 46 138

Urban 19 51 60 27 15769 92 113 126 400

In Exercise #7 on Class Handout Homework #3, this data was saved into an SPSS data file named tvchannels.

(a) If there were an association between area of residence and preferred television channel, then describe what could be said about how the distribution of proportions preferring the different channels would compare among the various areas of residence.

(b) The data are to be used to perform a hypothesis test to see if there is any evidence of an association between area of residence and channel preference. A 0.05 significance level is chosen. With the data file tvchannels, where each line of the data file represents a combination of categories of residence and channel preference, with the appropriate guidelines in the document titled Using SPSS Version 19.0, and with the steps in part (b) of Exercise #18 as a guide, use SPSS to do the necessary calculations and to create an appropriate graphical display.




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(c) Explain how we know that the sample size with the given data is sufficiently large for the chi-square hypothesis test in part (b) to be appropriate.

(d) Summarize the results (Step 4) of the hypothesis test in part (b) to see if there is any evidence of an association between area of residence and preferred television channel, with = 0.05. Then, indicate whether or not it is necessary to describe the relationship, and say why or why not. If necessary, use the standardized residuals to describe the relationship.



(a) Of the four separate analyses to be done, identify the one where a chi-square test for association could be used.

(b) Answer #1, and also indicate whether the hypothesis test should be one sided or two sided.

(c) Answer #2.

(d) Answer #3 and #4; when answering #4, note that we discussed no alternative test, but you should be able to state the primary assumption required to be satisfied.


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(e) Answer #5 by using SPSS to do the appropriate calculations and attaching the SPSS output to this assignment; be sure to include Cramer’s V in the output. (For the variable marital status, be sure to use the variable named MStatus in the SPSS data file, and not the variable named MStatus_Rec.) At the top of the printout, write a title in the following format:


(f) Answer #6 by writing a paragraph summarizing the results of the chi-square test for association; if necessary, use standardized residuals to describe the association, but if not necessary, explain why not; finally, give an interpretation of Cramer’s V for the data. Pattern the paragraphs after the summaries of results in Exercises #9 and #10 on Class Handout #4.


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(g) Answer #7 by using a word processor to create a contingency table below displaying the observed frequencies. Your table should be of a quality that is appropriate to place in a paper that you are submitting for publication. Immediately below that table, indicate the chi-square test statistic value with degrees of freedom, the p-value, and the value for Cramer’s V.


21. A researcher wants to study a possible relationship between age and salaryamong CEOs (chief executive officers for small companies). The data, which will be treated as coming from a random sample, is stored in the SPSS data file ceo.sav used with Class Handout #3 and available from the course web page schedule. A 0.05 significance level will be used for all hypothesis testing.

(a) After examining the data, complete the following table by listing in the first column each variable involved in the analysis, indicating in the second column whether each variable should be treated as qualitative or quantitative, and indicating in the third column whether each variable is a dependent variable, independent variable, or neither:

Variable(s) Type Dependent / Independent / Neither

(b) Give the name of an appropriate hypothesis test (including any possible follow-up analysis), and give the name of any appropriate alternative hypothesis test, if there is one. For each hypothesis test named, indicate whether the test is parametric or nonparametric.

(c) State the null and alternative (research) hypotheses to address what the researcher wants to study, and also indicate whether the hypothesis test should be one sided or two sided.


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(d) With the appropriate guidelines in the document titled Using SPSS Version 19.0, use SPSS to do the appropriate calculations and to create an appropriate graphical display for the data used in this hypothesis test; then attach the SPSS output to this assignment. At the top of the printout, write a title in the following format:

Your Name - Math 214(your section) - Today's DateClass Handout #4 Homework - Exercise #21(d)Textbook Chapter 1

(e) State the assumption(s) that must be satisfied for the hypothesis test you selected, and summarize what information, if any, is available about the assumption(s) from the SPSS output.

(f) Write the results of the hypothesis test in a format that is suitable for a paper that you are submitting for publication; be sure to include relevant information about the test statistic, sample statistics, and p-value, and an appropriate summary of follow-up analyses, if necessary.




22. A researcher wants to study a possible relationship between the penetrationweight of water through paper towels and the brand of paper towel. The data consists of a random sample of penetration weights for each of four brands of paper towels, and this data is displayed below. A 0.05 significance level will be used for all hypothesis testing.

Brand Penetration Weights (grams)

Tuff 112 104 110 108 112 114

Econ 120 116 122 114 112 118

Cheep 106 114 110 108 116 112

Super 120 110 112 112 114 116



(b) Give the name of an appropriate hypothesis test, and give the name of any appropriate alternative hypothesis test (including any possible follow-up analysis), if there is one. For each hypothesis test named, indicate whether the test is parametric or nonparametric.


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(d) Enter this data into an SPSS data file; then with the appropriate guidelines in the document titled Using SPSS Version 19.0, use SPSS to do the appropriate calculations and to create an appropriate graphical display for the data used in this hypothesis test; then attach the SPSS output to this assignment. At the top of the printout, write a title in the following format:





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23. A researcher wants to study voters’ opinions about a bill related to smoking in public places, which is currently being considered by the state legislature. Randomly selected voters are polled in order to collect data, where each voter is asked to choose one of the following opinions about the bill: strongly opposed, somewhat opposed, neutral, somewhat favor, and strongly favor. The purpose of the research is to see if there is any evidence against the claim that the proportion of voters in each opinion category is the same. The data is stored in the SPSS data file bill.sav available from the course web page schedule. A 0.05 significance level will be used for all hypothesis testing.





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24. A researcher wants to study a possible relationship between sex of the voterand opinion about the bill described in Exercise #13. The data to be used is stored in the SPSS data file bill.sav used in Exercise #13 and available from the course web page schedule. A 0.05 significance level will be used for all hypothesis testing.






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25. A researcher wants to study how expenses and sales compare for the chainof restaurants McDoogle’s. The data will come from the 30 randomly selected restaurants in Exercise #3 on Class Handout #4, and this data is stored in the SPSS data file chain.sav created in Exercise #3 on Class Handout Homework #3. The purpose of the research is to see if there is any evidence of that the mean profit (sales minus expenses) is significantly greater than zero. A 0.05 significance level will be used for all hypothesis testing.






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26. For each of the following, indicate the parametric and nonparametric statistical analysis which could be appropriate:

(a) A standard treatment for an ailment is being compared with two new treatments labeled "New A," and "New B." A 0.05 significance level is chosen for a hypothesis test to see if there is any evidence of a difference in the proportion of complete cures. The data observed on a group of subjects treated as a simple random sample have been organized into a table with two rows (labeled “cure complete” and “cure not complete”) and three columns (labeled “standard treatment”, “new A treatment”, and “new B treatment” ).

(b) Knowledge about good nutrition habits is to be compared among three different high schools: Central high school, Grandview high school, and Sandler high school. A 30-item questionnaire is administered to randomly selected students at each school, and the number of correct responses for each student is recorded. A 0.10 significance level is chosen for a hypothesis test to see if there is any evidence of a difference in mean score among the high schools.

(c) A 0.05 significance level is chosen for a hypothesis test to see if the mean length of ball bearings produced by the Nuketown factory is larger than for those produced by the Highville factory. A simple random sample of ball bearings produced by each of the two factories is recorded (in inches).


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(d) A hypothesis test is to be performed to see if there is any evidence that the four political party categories Republican, Democrat, Independent, and Other, are not equally likely among voters in a state.

(e) A particular company has chosen a 0.05 significance level to see if there is any evidence that the mean number of sales per salesperson tends to be higher in Bombsville than Slumsville. Several salespersons were each assigned to both cities for one week. The number of sales for each salesperson in each city was recorded.

(f) The customers who buy apples at a supermarket have a choice of red apples or green apples. A hypothesis test is to be performed to see if there is any evidence that the different types of apples are not equally preferred.


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