SPSS^{TM} Practice Set
Instructions and Answers

Other SPSS Learning Sites
SPSS Starter KitUCLA Statistics Using SPSS Video Lectures Quick Notes SPSS Statistics Course Materials Return to Statistics Internet Library Visit Academic Subjects Libraries  
Chapter 2 Summarizing Data.
Problem I message:
SPSS will do an array.
We will skip part 2 and let SPSS set the class width.
Others must create a data file for CD sales. You may want to review creating a data file on page 1 of Quick Start for SPSS. I named my data file spss006 for the software being used and the problem's page number. I named my variable "cdsales." All SPSS users should choose Data, Sort Cases, double click on cdsales, and accept the default Ascending by choosing OK. See page PS 6 and 7 for the answer. Problem II message: SPSS will determine a 3 class frequency distribution for this data. SPSS procedures to change the number of classes will not be explored. Practice set graphs for the actual data and not the frequency distribution may be done using SPSS. As a result, SPSS answers to Problem I can not be checked. All SPSS users should choose Statistics, Summarize, and Explore. Click on the right button to load cdsales into the Dependent List. Click on the Statistics rectangle, click on the Grouped frequency tables bull'seye, and choose Continue. Choose Plots, make sure Stemandleaf is checked, choose Continue, and choose OK for a 3 class frequency table. All SPSS users should choose Graphs from the main menu. Choose Bar, Simple, and Define. Click on the right button to load the variable (cdsales) into the Category Axis box. Accept the default N of cases and choose OK. After viewing this ungrouped vertical bar chart choose discard. Choose Graphs, Bar, Simple, and Define. This time choose Cum n of cases and choose OK. After viewing this cumulative bar chart try the 2 percentage graphs. Repeat this process for line, area, and histogram graphs. Saving Charts is easy. To save the current graph choose File and Save As. Type spss006 in the File name box and SPSS will add cht as an extension. The file spss006.cht will be stored on the a: drive. This file can be used by choosing File, Open, and Charts. If necessary, use the scroll bar to select the a: drive and then double click on the desired chart. Chapters 3 and 4 Measuring Central Tendency and Dispersion of Ungrouped Data Problems message: SPSS will calculate many of these statistics. Those using Quick's data files should load spss006 by choosing File, Open and Data. Use the scroll arrow next to the Drives box to highlight the a: drive. Load by double clicking on spss006. Others should load their page 6 data file. All SPSS users should choose Statistics, Summarize, and Frequencies from the main menu. Use the right button to load cdsales into the variable column. Select the Statistics button at the bottom of the screen. Click on every empty box so all available statistics will be calculated. Quick Notes Statistics has or will explore many of these statistics. After you check the Percentiles box, it will be necessary to type a percentage in the space provided. Type in 60 because you are asked to calculate the 6th decile on page 13 of Quick Notes Statistics. Click the Add button. Check remaining squares, Continue, and OK. Practice Set 3 answers: 1A) 17 4) 16 5) 16 7A) 14 7B) 21 7D) 17 Do other problems by hand. Practice Set 4 answers: 1A) 21 1C) 30.6 1D) 5.532 Do other problems by hand. Print the statistics by choosing the print icon below the SPSS main menu. Printer Setup is located under File of the main menu.
Chapters 5 and 6 Measuring Central Tendency and Dispersion of Grouped Data Chapters 5 and 6 problems are very similar to those of chapters 3 and 4. These SPSS Practice Set Instructions and Answers will explore only the ungrouped Practice Sets of chapters 3 and 4. Part II Practice Sets on Probability
Expect minor rounding differences between Quick answers and SPSS answers. 

Part II Probability Chapters 7 & 8 Practice Problems and Quick Questions do not require SPSS but are good to Review Principles


Chapter 9 Discrete Probability Distributions Problem I message: These problems should be done by hand.
Problem II message: SPSS will calculate binomial probabilities. All SPSS users should select Transform and Compute. Name the Target Variable cumsale3. Use the scroll bar beside the Functions box to find CDF.BINOM(q, n, p). Highlight it and use the up button to load it into the Numeric Expression box. Set q to 3 (success), n to 5 (trials) and p to .6 (probability of success). Choose OK and answer OK to the question concerning changing existing variables. SPSS will replace the 3 in the data matrix with the cumulative probability for 03 sales (.663). Repeat this process for 2 successes in 5 tries (answer is .317). Subtract these answers for the probability of exactly 3 sales. Problem III and IV message:
These problems may be done following problem II procedures. They are more easily done with the
Binomial table on page ST 1 or a cumulative Binomial table in a traditional statistics book. Those using Quick's data files should load spss055 by choosing File, Open, and Data. Use the scroll bar next to the Drives to locate and click on a:. Double click on spss055. Others must create a data file with 8 variables for the 8 possible outcomes of this distribution. Choose Data and Define Variable and name your variables comp0 to comp7. Choose Type and set the number of decimal places to 4. Set the value of each variable to 07 respectively. All SPSS users should select Transform and Compute. Name the Target Variable comp0. Use the scroll bar beside the Functions box to find CDF.POISSON (q, mean). Highlight it and use the up button to load it into the Numeric Expression box. Set q equal to 0 (success) and the mean equal to 1. Choose OK and answer OK to the question concerning changing existing variables. SPSS will replace the 0 in the data matrix with the probability of having 0 complaints in a 20 minute period when the mean is 1 complaint per 20 minute period. Calculate the other probabilities in a similar manner. Problem VI message: Problem VI may be done following problem V procedures although it is easier to do with the Poisson table on page ST 2 of Quick Notes Statistics. 
 
Chapter 10 Continuous Normal Probability Distributions Problem I message: SPSS will calculate probabilities associated with a normal distribution. Those using Quick's data files should load spss062 by choosing File, Open, and Data. Use the scroll bar next to the Drives to locate and click on a:. Double click on spss062. Others must create a data file with 5 variables. Choose Data and Define Variable. Name your variables comp1, comp2a, comp2b, comp3, comp4a, and comp 4b. Choose Type and set the number of decimal places to 4. Let each variable equal 15 respectively. All SPSS users should select Transform and Compute. Name the Target Variable comp1. Use the scroll bar beside the Functions box and the up button to load CDFNormal(q, mean, stddev) into the Numeric Expression box. Set q to 15000 (be sure not to use a comma), the mean to 25000, and the standard deviation to 5000. Choose OK twice. Note that SPSS gives the probability of commissions being lessthan $15,000. For the answer to part A subtract .0228 from .5000. Probabilities needed to answer parts BD can be solved following these procedures. Problem II and III message: These problems should be done by hand 
Problem I message: SPSS will calculate a confidence interval for the mean of a sampling distribution. Those using Quick's data files should load spss068 by choosing File, Open, and Data. Use the scroll bar next to Drives to locate and click on a:. Double click on spss068. Others must create a data file for the page 68 data. You may want to review creating a data file from page 1 of Quick Start for SPSS Create a data file using 36 rows and 1 column. I named my variable "weight." When saving the file, I named it spss068 for the software being used and the problem page number. All SPSS users should select Statistics, Compare Means, and OneSample T Test. Double click on weights (or use the right arrow button) to copy the file into the Test Variables box. Be sure your software is set for the 99% Confidence Interval by choosing Options. If it isn't, type 99 in the % block, choose Continue, and choose OK. Problem II message: Redo problem I with a 95% confidence interval. Problem III message: Answer this problem by hand. 
 
Chapter 12 Sampling Distributions Part II Problem I message: This problem can be answered by following Practice Set 11 instructions. Those using Quick's data files should load spss072 by choosing File, Open, and Data. Use the scroll bar next to Drives to locate and click on a:. Double click on spss072. Others must create a data file for page 72. Data entered should consist of a 1 for passed and a 0 for failed. The variable inspect must now be defined. Double clicking on var00001. Type inspect in the Variable Name box. In the Change Settings section choose Labels. Type Parts Inspection in the Variable Labels box, type 0 in the Value box, type passed in the Value Label box and choose Add. Next, type a 1 in the Value box, type failed in the Value Label box, choose Add. Choose Continue, and OK. In the next data matrix column enter a 0 next to samples that passed (lessthan or equal to 30 mg) and a 1 for those that failed (greater than 30 mg). All SPSS users should choose Statistics, Compare Means, and OneSample T Test from the main menu. Double click on inspect (or use the right arrow button) to copy it into the Test Variable box. Be sure your software is set for the 95% Confidence Interval by choosing Options. If it isn't, type 95 in the % block, choose Continue, and choose OK. Problem II, III, and IV message: Answer these problems by hand. 

 
Chapter 13 Large Sample Hypothesis Testing Problem I message: This is a one sample test of a mean. SPSS assumes a small sample and calls the calculated z for this test statistic a t value. Ignore this for now. We study the small sample t distribution in chapter 16. Those using Quick's data files should load spss068. Others should load their page 68 data file. All SPSS users should choose Statistics, Compare Means, and OneSample T Test. Highlight weight and copy it into the Test Variable box using the right button. Set the Test value to 30 mg. Choose Continue and OK. The tvalue of 2.32 is not beyond 2.33 (it is less than 2.33 ) and H_{0} is accepted. Parts are not too heavy. I use the term beyond to indicate further from H_{0}, the hypothesized population parameter. Problem II message: If a 1tail test is accepted then the 2tail test must be accepted. Here, 2.32 < 2.58 and H_{0} is accepted. Problem III message: Redo problem II with the new level of significance. Here, 2.32 > 1.96 and H_{0} is rejected. 
 
Chapter 14 Large Sample Hypothesis Testing Part II Problem I message: This problem tests the difference between 2 independent means. Those using Quick's data files should load spss090. Others should create a data file with 70 rows and 2 columns (variables). In the first data variable column entitled days enter the data for Supplier A and then the data for Supplier B. In the second source variable column entitled supplier, enter a 0 next to Supplier A's data and a 1 next to Supplier B's data. This source variable may be defined in a similar manner as the Practice Set 12 source variable. All SPSS users should select Statistics, Compare Means, and IndependentSamples T Test. Use the right button to load days into the Test Variable box and supplier into Grouping Variable box. Select Define Group. Set Group 1 to 0 and Group 2 to 1. Choose Continue and OK. Accept H_{0} because the test statistic t (z) of 1.32 (for unequal variances) is not beyond 1.96 (it is greater than 1.96), the critical value of t (z). Delivery times are the same. Problem II message: SPSS calculates z and p simultaneously. We must redo the chapter 13 test and look for the p value. Those using Quick's data files should load spss068. Others will need to load their page 68 data set. All SPSS users should redo the chapter 13 z (t) value test as a pvalue test. Choose Statistics, Compare Means, and OneSample T Test. Highlight weight and load it using the right button. Set the Test value to 30 mg. Choose OK. SPSS gives a twotail pvalue using t of .026 which is .013 for a onetail problem. Accept H_{0} because .013 > .01. Quick's manual solution gives a onetail pvalue using z of .0103 which also accepts H_{0}. Parts were not too heavy. Problem III message: Answer this problem by hand. 
Written Problems
 
Chapter 15 Hypothesis Testing of Population Proportions Problem I message: The population proportion is a type of mean so these problems use the same onesample mean test described by chapter 13 directions. SPSS users should load spss096. Others should create a data file using a one for parts that passed and a zero for those that failed. All SPSS users should do a OneSample T Test of the variable passed. Use .86 as the Test Value. The p value of .355 is for two tails. P/2 = .355/2 = .178 > .01 and H_{0} is accepted. The proportion of parts passing inspection has not increased. Problem II message: This is a 2 sample proportion test similar to those explored in chapter 14. Those using Quick's data files should load spss096. Others should create a data file with 200 rows and 2 columns variables). In the first column entitled defects, enter the data for the day shift and then the data for the night shift. Enter a 0 for passes and a 1 for failed. For the source variable enter a 0 for day shift data and a 1 for night shift data. When defining the source variable, follow the procedures described in chapter 14. All SPSS users should run an IndependentSample T Test using practice set 14 procedures. P of .03 is for two tails. Because .03 > .01, accept H_{0}. Shift defects are the same. 
 
Chapter 16 Small Sample Hypothesis Testing Using Student's t Test  
Problem I message: This is an analysis of 2 independent means. It is similar to problems done earlier. Those using Quick's data files should load spss100. . Others should create a data file containing both a data variable and a source variable using procedures discussed earlier. All SPSS users should run an IndependentSample T Test using practice set 14 procedures. Be sure to define group 1 as 0 and Group 2 as 1. The t value of  4.16 (for unequal variances) is beyond the critical value of 2.831. P is .000. H_{0} is rejected, sick days taken were not the same. Problem II message: This is a paired difference test. Those using Quick's data files should load spss100. Others should add 2 variables to spss100, one for the efficiency rating before training and the other for the efficiency rating after training. Be sure to match each employee with their before and after efficiency rating. All SPSS users should choose Statistics, Compare Means, and PairedSample T Test. Highlight both the Before and After variables and then use the right button to move these variables into the Paired Variables box. Choose OK. H_{0} is rejected because p of .003/2 = .0015 < .01. Training increased efficiency. 
Written Problems
Problems Requiring SPSS
 
Problem I message: This is a Quality Control problem. Those using Quick's data files should load spss104. Others should create a data file with the 12 samples in column 1. A source variable should have the numbers 112.All SPSS users should choose Graphs and Control. Choose XBar, R, s, and Define. Move weight into Process Measurement and sample into Subgroups Defined by. Choose OK. See page PS 105 for the answer. To see the R chart use the scroll bar at the top of the page to select Range of weight by sample. See page PS 105 for the answer. Problem II message: As defined, this problem can not be done with SPSS. Actual data is needed. See page PS 106 for the answer.  
Problem I message: This twosample analysis of the variance is similar to the two sample analysis of the mean conducted earlier. This problem should be done by hand. Problem II message: This is a oneway analysis of variance (ANOVA). Those using Quick's data files should load spss111. Others should create a page 111 data file with one variable for weight data and one for source (department) data. All SPSS users should select Statistics, ANOVA Models, and Simple Factorial. Move weight data into Dependent and dept into Factor's). Select Define Range and set the minimum to 1 and the maximum to 3. Choose Continue and OK. H_{0} is rejected because p of .002 < .05. Part mean weights are not equal. 
Problems Requiring SPSS
Written Problems
 
Problem I message: This is a twoway analysis of variance (ANOVA). Those using Quick's data files should load spss116. Others should create a 3 variable file containing data on weight, department(dept), and time. When doing time, be sure to match each time with the appropriate department and weight. All SPSS users should select Statistics, ANOVA Models, and Simple Factorial. Move weight into Dependent, department(dept) into Factor(s), and time into Factors(s). Click on the factor variables and define them with limits of 1 to 3. Choose Continue and OK. SPSS provides the data needed to calculate F. See page PS 117 for the answer. Problem II message: Do this problem by hand. See page PS 117 for the answer.  
Chapter 20 Nonparametric Hypothesis Testing of Nominal Data Problem I message: This is a nonparametric test using ChiSquare.
Those using Quick's data files should load spss122. All SPSS users should select Statistics, Nonparametric Tests, and ChiSquare. Load the source variable into the Test Variable List box. Highlight the bull's eye next to Value in the Expected Values section. Insert .2 and choose Add. Repeat process inserting .3 and .5. Choose OK. Because 1.03 < 9.21, accept H_{0}, defects follow Darin's proposed distribution. Problem II message: This problem emphasizes the concept of statistical independence. Those using Quick's data files should load spss122. Others should create a 2 variable data file. The first variable entitled sales consists of twentyfour 1's for Young Sale and sixteen 0's for Young No Sale. Below this data put twelve 1's for Older Sale and eight 0's for Older No Sale. The second variable entitled age consists of forty 0's for Young and twenty 1's for Older. All SPSS users should select Statistics, Summarize, and Crosstabs. Copy sales into Row(s) and age into Column(s). Choose Statistics and check Chisquare. Choose Continue and OK. Chi square is zero and H_{0} is accepted. Making a sale and age are independent. Because the buying percentage of each part of the population (60% or .6) exactly equals the buying percentage of entire population(60% or .6), chi square is zero.  
Answers provided by http://www.textbooksfree.org/  
Chapter 21 Nonparametric Hypothesis Testing of Ordinal Data Part I Problem I message: This is a run test to determine randomness. This data on part weight was first presented on page 68.
Those using Quick's data files should load spss128. All SPSS users should select Statistics, Nonparametric Tests, and Run. Load weights, accept the Median as the cut point, and choose OK. Using different methods, both SPSS and Quick accept the null hypothesis that parts were drawn at random. Problem II message: Do this one sample median test by hand and see page PS 128 for the answer. Problem III This is a two sample medians test.
Those using Quick's data files should load spss128. All SPSS users should select Statistics, Nonparametric Tests, and 2 Independent Samples. Load sickdays into the Test Variable List box and educa into the Grouping Variable box. Define Group 1 as 0 and Group 2 as 1. Choose Continue. Accept MannWhitney U as the default by choosing OK. Because .0012 < .01, reject H_{0}, there is a difference in median sick days. 
Test Problems requiring
SPSS  
Chapter 22 Nonparametric Hypothesis Testing of Ordinal Data Part II Problem I message: This is a paired sample (difference) test of the median.
Those using Quick's data files should load spss133. All SPSS users should select Statistics, Nonparametric Tests, and 2 Related Samples. Highlight the before variable and the after variable and then use the right button to load them into the Test Pair(s) List box. Choose the sign test and choose OK. SPSS gives the probability of 2tails. Accept because .065/2 = .0325 > .01. Efficiency did not change. Problem II message: This is a KruskalWallis test of several medians.
Those using Quick's data files should load spss133. All SPSS users should select Statistics, Nonparametric Tests, and K Independent Samples. Load weights into the Test Variable List box and depts into the Grouping Variable box. Define the Range for Grouping variables as 1,3 and choose Continue. Accept the KruskalWallis default by choosing OK. Reject H_{0} because .0056 < .01. Medians are not equal. 

 
Problem I message: SPSS will calculate the coefficient of correlation. Those using Quick's worksheets should load spss148. Others should create a data file with 2 variables. The first should contain employee ages and the second employee sales. All SPSS users should select Statistics, Correlation, and Bivariate. Load age, sales, and choose OK. r = .9096 Other questions should be done by hand. Answers are on page PS 148 of Quick Notes Statistics . 
Problems Requiring SPSS
Test Problems requiring SPSS
 
Chapter 24 on Regression Analysis Problem I message: SPSS will calculate the information needed to write the regression equation. Those using Quick's worksheets should load spss148. Others should load their page 148 worksheet. All SPSS users should choose Statistics, Regression, and Linear. Copy sales into the Dependent box and age into the Independent box. Choose OK. a = 55.94 and b = 1.07. RSq = .82 Other questions should be done by hand. Answers are on page PS 154 of Quick Notes Statistics. 
Inferential Statistics Test Page
138 Page 139 Page
140
Page 141 Test Answers
Page T138 Page T139
Page T140 Page 141 
Exam Source

Review Stuff
Categorizing Statistics
Problems 
SPSS Quick Questions Answers Note: When Quick Questions can not be done with SPSS and should be done by hand, reference has been made to the page in Quick containing the solution to the question.  
Chapter 1  See page QQ 3. 
Chapter 2  2A) 6, 14, 17, Free Sample 3, 26, 27, 31, 33, 34, 37, 38, 38, 44, 46, 48, 54 Other answers on page QQ 8. 
Chapter 3  2A) 7 2B) 7.5 2C) 8 6A) 5.25 6B) 8.75 6D) 4.6 6E) 9.65 Other answers on page Q 14. 
Chapter 4  2A) 5.143 2B) 2.268 See page QQ 20 for other answers. 
Chapter 5, 6  See page QQ 28 and 32 for these answers. 
 
Chapter 7  See page QQ 44 and 45 for these answers. 
Chapter 8  See page QQ 50 and 51 for these answers. 
Chapter 9  3A) .9988  .9774 = .0214 4B) .1353 4C) .6767  .4060 = .2707 See page QQ 56 for other answers. 
Chapter 10  1A) .8413 1B) 1.9772 = .0228 1C) .0054  .0013 = .0041 1D) .5000 See page QQ 64 for other answers. 
Chapter 11  3A) Using t, 48.91  61.09 3B) Using t, 46.829  63.171 See page QQ 97. 
Chapter 12  1) See page QQ 74. 2A) .621  .879 2B) .653  .847 
 
Chapter 13  1) See page QQ 87 and 92. 2A) t = 5, reject H_{0} , bulbs last < 20,000 hours 2B) t =  2.5, reject H_{0} , weekly earnings changed 
Chapter 14  2) t = 2.63, reject H_{0} , sales time is not the same 3) p/2 =.119/2 = .0595 > .05, accept H_{0} , tires last > or = to 70,000 miles 4) p/2 = .14/2 = .07 > .05 accept H_{0} , loan length did not increase See page QQ 87, 92 and 93 for other answers. 
Chapter 15  2) using the sample sigma of .368 yields p =.185/2 = .0925 > .05, accept H_{0} , P is not < the national average 3) p = .0150 < .05, reject H_{0}, defined rentals differ at these stores See page QQ 97 for other answers. 
Chapter 16  1) See QQ 101. 2) t = 1.73 < 3.143, accept H_{0}, sick days did not decrease 3) t = .93 which is not beyond 1.753, accept H_{0}, women did not do better than men 
Chapter 17  See page QQ 106. 
Chapter 18  3) p = .011 < .05, reject H_{0}, means are not equal See page QQ 112 for other answers. 
Chapter 19  2B) Use mean square data provided by MINITAB to calculate F. See page QQ 118. 
Chapter 20  2) p = .0000 < .05, reject H_{0}, distributions are not similar 4) p = .00004 < .01, reject H_{0}, course and grades are dependent See page QQ 124 for other answers. 
Chapter 21  1) p = .098 > .01, accept H_{0}, parts were drawn at random 2) See page QQ 130. 3) p = .3926 > .05, accept H_{0}, median delivery times are the same 
Chapter 22  1) p = .2218 > .10, accept H_{0}, employee absenteeism has not changed 2) p = .0027 < .01, reject H_{0}, median grades are not equal 
 
Chapter 23  4A) r =.8893 4B) .791 Other answers on pages QQ 150 and 151. 
Chapter 24  3) a = 1.81 and b = .282 See pages QQ 156 and 157 for other answers. 
SPSS Exam 1 Answers Problems that can not be done with SPSS and should be done by hand are so marked. Answers to these problems begin on page T 35 near the end of Quick Notes Statistics. 
14) Do by hand. 5) The SPSS frequency distribution and graphs will differ from those in Quick. 6A) Mean = 7 6B) Median = 6 6C) Mode 6 6D) Variance 18.857 6E) Standard deviation = 4.342 6H) Skewness (not Pearson's) = 2.093. Answer other questions by hand. 
SPSS Exam 2 Answers 
1A) .9987  .5000 = .4987 1B) .0951 1C) .9772  .9332 = .0440 210) Do by hand. 11A) .7351 11B) Inserting 1 and choosing cumulative probability yields .9672 and 1  .9672 = .0328 11C) See the distribution located on page ST 1 of Quick Notes. 11D) .9978  .9672 = .0306 12A) Inserting 1 and using cumulative probability yields .0916. 12B) See the page ST 2 table which may be used to draw the page T 8081 graph. 13) See page T 82 for answers to these questions. 14) See page T 82 for answers to these questions. 15) A 1Sample t test using Compare Means under Statistics yields a range of 6.89 to 8.31. 16A) A 1Sample t test using Compare Means under Statistics and a Sigma of .4629 yields a range of .59 to .81. 16B) Do this problem by hand. 

1) t = 1.14 and p/2 = .261/2 = .13 > .01, accept the Null Hypothesis, the mean is greater than or equal to $8.00 2) using a standard deviation of .463, t = 1.53 and p/2 = .133/2 = .067 > .05, accept the Null Hypothesis, the mean could be greater than or equal to 80%. Note that Quick Notes Statistics rejects the null hypothesis. This is because Quick uses the population standard deviation to estimate the standard error and SPSS uses the sample standard deviation. 3) Do by hand. 4) t = 4.24 and p/2 = .024/2 = .012 < .05, reject the Null Hypothesis, sales performance improved 5) t = 2.97 and p = .004 < .05, reject the Null Hypothesis, mean service time at these stores is not the same 6) t =  4.0 and p = .001 < .01, reject the Null Hypothesis, assembly time has gone down 7) Do by hand. 8) ChiSquare = 3.1429 < 9.49 and p = .5342 > .05, accept the Null Hypothesis, accidents happen equally throughout the week 9A) F = 5.77 and p = .024 < .05, reject the Null Hypothesis, the mean time to assemble computer parts is not equal for these three departments 9B) Do by hand. 10) p = .1224 > .01, accept the Null Hypothesis, assembly times are equal 11) Chi square = 11.23 and p = .0036 < .01, reject the Null Hypothesis, median assembly times for these three methods are not equal 12) SPSS control charts look very similar to those on page T 145. 13) p = .2188 > .10, accept the Null Hypothesis, customers rate these brands equally 
SPSS Exam 4 Answers 
1 and 2) Do by hand. 3A) r = .885. 3B and C) Do by hand. 4) Do by hand. 5) The SPSS scatter graph is similar to the graph on page T 160. 6A) a = 13.51 and b = 6.54 6B, C, D, and E) Do by hand. 