Class Handout #4 Homework Name ______

Class Handout #4 Homework Name ______

Exercise #1

Read Part 1 of the “PRACTICAL EXERCISES” section at the end of Chapter 1. You should find that four separate analyses areto 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 onesided or twosided.

(c)Answer #2.

(d)Answer #3 and #4.

Exercise #1 - continued

(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.

(f)Answer #6 by writing a paragraph patterned after the one used to answer Exercise #1 on 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.)

Exercise #2

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

(b)Answer#1, and also indicate whether the hypothesis test should be onesided or twosided.

(c)Answer #2.

(d)Answer #3 and #4.

Exercise #2 - continued

(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.

(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 summarizingthe results of the nonparametric analysis. Pattern each paragraph after the summaries of results in Exercises #3 and #4 on 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.)

Exercise #3

Read Part 2 of the “PRACTICAL EXERCISES” section at the end of Chapter 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.

(b)Answer #1, and also indicate whether the hypothesis test should be onesided or twosided.

(c)Answer #2.

(d)Answer #3 and #4.

Exercise #3 - continued

(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 calculationsand to create an appropriate graphical display, and attaching the SPSS output to this assignment.

(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 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.)

Exercise #4

The mean length of fish is being studied for North Lake, Blue Lake, and Harvey 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:

North13 17 15 18 17

Blue15 12 16 11 16

Harvey14 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.)

Exercise #5

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:

Deluxe165 162 159 162

Econ156 163 158

Nogood151 154 160

(a)Use SPSS to perform the necessary calculations for this hypothesis testand 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.

Exercise #5 - continued

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 ANOVAfor Mean Breaking Strength

with Three Rope Types

Exercise #5(a) of Class Handout #4 Homework

Your 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 Explorein the SPSS output, and edit the title so that it is in the following format:

Box Plots of Breaking Strengthwith Three Rope Types

Exercise #5(a) of Class Handout #4 Homework

Your 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 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.

Exercise #5 - continued

(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 oneway ANOVA. Next, in a second paragraph, summarize the results (Step 4) of the f test in the oneway 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 methodin 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.)

Exercise #6

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.)

(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.)

Exercise #7

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 oneway ANOVA together with a Bonferroni multiple comparison (if necessary)could be used, or a KruskalWallis 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.

(d)Answer #3 and #4.

Exercise #7 - continued

(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 testswith corresponding multiple comparison procedures mentioned in part (a).

(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.

(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.)

Exercise #8

Randomly selected customers of a car dealership are polled in order to collect 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 toperform 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 testand 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.

Exercise #8 - continued

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 Between

Car Color Preference and Area of Residence

Exercise #8(b) of Class Handout #4 Homework

Your 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 3:

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

Stacked Bar Chart for Distribution of

Car Color PreferencesAmong Areas of Residence

Exercise #8(b) of Class Handout #4 Homework

Your 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:

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.

Exercise #8 - continued

(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.

Exercise #9

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

Channel Preference
Residence / Cartoon / Comedy / SciFi / Western
Rural / 28 / 7 / 17 / 53 / 105
Suburban / 22 / 34 / 36 / 46 / 138
Urban / 19 / 51 / 60 / 27 / 157
69 / 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 toperform 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 #8 as a guide, use SPSS to do the necessary calculations and to create an appropriate graphical display.

Exercise #9 - continued

(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.

Exercise #10

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 chisquare 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.