Question

Use SPSS for this exam, be sure to include all the following information to get full credits: (1) null and alternative hypotheses (15%) (2) nameofthe test(15%, explain why you chose it) (3) thetest statistic and its degree offreedom or ANOVAtable(if applicable) (30%! (4) p-value (15%), and (5) scientific conclusion (25%, using 0.05 significance). 1. Ostriches live in hot environments, and they are normally exposed to the sun for long periods Mammals in similar environments have special mechanisms for reducing the temperature of their brain relative to their body temperature. The mean body and brain temperature of six ostriches was recorded at typical hot conditions. The results, in degrees Celsius, showed in the following table (create your own data file) Ostrich Body temperature Brain temperature 38.51 39.32 2 38.45 39.21 38.27 39.20 3 38.52 4 38.68 38.62 5 39.09 38.84 6 38.18 (a) Test whether ostriches body temperature is equal to 38.5 degree Celsius. Report the 90% confidence interval for the mean body temperature. (10 pts) (b) Test whether any difference in temperature between body and brain for these ostriches. (Note: use ONE method you think the most appropriate and explain your answer.) (10 pts) 2. The following table lists total sales of a specific merchandise in six stores during four seasons (Final_Q2.sav) Sales (in thousand dollars) Fall Winter Summer Young Adults Young Adults Young Adults Young Adults 68 57 54 59 69 60 79 68 67 64 63 80 67 58 65 78 79 62 63 76 63 64 72 81 57 60 78 61 68 78 74 78 60 75 59 63 84 58 57 81 83 61 63 (a) Apply an appropriate analysis of variance to this data, justify your choice, and report the complete ANOVA table (must include Source, SS, DF, MS, F, and p). (10 pts) (b) Test the null hypothesis that the sales are the same for all seasons surveyed. (5 pts) (c) Assume that the winter is a control group. Use an appropriate test to compare the control mear sales with the other means, and conclude which season's sales is different from winter. (10 pts) 3. Use the data in the attached file (Final_Q3.sav) with 10 data points of Y and x1, X2, X3, X4, and X5 (a) Fit a simple linear model of Y on one independent variable X2 only, report (1) the Y intercept and regression coefficient; (2) test Ho: B 0. (10 pts) (b) Fit a full linear model of Y on ALL Xs, report (1) the Y intercept and partial regression coefficients; (2) test if there is a significant multiple regression relationship between Y and Xs; (3) test Ho: B3 0 (for X3). (15 pts) (c) Compare the two models in part (a) and (b), which one do you think fits the data better? Explain your answer. (5 pts) (d) Analyze and test whether the independent variables x2 and X4 significantly correlated. If the value of X2 increases, how would the value of X4 change? (10 pts) 4. The sex of consecutive children is independent in humans. For example, having had one boy already does not change the probability that the next child will also be a body. So the number of sons and daughters in families containing two children would match a binomial distribution with n 2, and p-0.51 (probability of having a boy). n! n-k In a data from the National Longitudinal Survey of Youth, which compiles data on the sex of children in a random sample of families of different sizes. The following table shows the number of sons in 2 two-child families. 440 Number of boys Observed number of families Expected number of families (binomial) 530 1330 580 2 2440 Total (a) Calculate the expected number of families containing exactly two children that have 0, or 1, or 2 boys using the binomial formula (round to the nearest tenth, i.e., one decimal point). (5 pts) (b) Test the null hypothesis that the number of boys in two-children families surveyed follow a binomial distribution. (10 pts)

Answer 1

Answer:

1)

a)

蟋"Untitled! [DataSetO]-IBM SPSS Statistics Data Editor File Edit View Data Iransform Analyze Direct Marketing Graphs Utlities Add-ons Window Help Role Measure Ali Columns Missi Values Label Input Input WidthDecimals Scale Scale Scale Right Right Ostriches Numeric Body Temperat.. None Input 看Right 2 Body_Temp.. Numeric 8 Brain Temperat... None Brain_Temp. Numeric 10 12 13 14 15 16 17 18 19 20 21 23

As shown in above image declare variable Body Temperature and Brain Temperature as Numeric with 2 decimal and Scale measure

Untitled1 DataSet0]- IBM SPSS Statistics Data Editor File Edit View Data Transform Anlye Direct Marketing Graphs Utilities Add-ons Window Help LAI Reports 14 Descriptive Statistics Visible: 3 of 3 Variables Tables Ostriches Body Te Compare Means var var ature General Linear Model 38.5 1.00 Generalized Linear Models 2.00 38.4 Mixed Models 3.00 38.2 Correlate 4.00 38.5 Regression 5.00 38.6 38.1 Loglinear 6.00 Neural Networks Classity Dimension Reduction 10 Nonparametric Tests One Sample Forecasting 12 Independent Samples.. Survival 13 Related Samples... Multiple Response 14 Legacy Dialogs 15 Missing Value Analysis.. 16 Multiple Imputation 17 Complex Samples 18 Quality Control 19 ROC Curve 20 21 Go to Settings to activate Windows Variable View Data View IBM SPSs Statistics Processor is ready 8-30 PM rP ^恤瘺41 ENG 5/16/2019 O Type here to search

包"Untitled! [DataSetJ-BM SPSS Statistics Data Editor File Edit View Data Transform Analze Direct Marketing Graphs Utilities Addons Window Help At 14 3 Variables 20 Kolmogorov-Smirmov Test Options Ostriches Body_Tempei BrainOne-Sample N c Tests va ature Hypothesized Distributions 00 38.51 2.00 384500e Objective Fields Setings 로·Normal 38.27 Select an item: bution Parameters 3.00 4.00 38.52 Automatically choose the tests based on the data Use sample data Choose Tests 38.62 5.00 customize tests O Custom Test Options 6.00 38.18 Compare observed binary probability to hypothesized (Binomial test) Mean o Std Dey. 1 User-Missing Values Uniform Compare observed probabilities to hypothesized (Chi-Square test) Distribution Parameters 10 Use sample data Test observed distribution against hypothesized (Kolmogoro-Smirnov test)| | OCustom 12 Optons Min: □ Compare median to hypothesized (Wilcoxon signed-rank test) 14 Exponental Poisson Hypothesized median Mean ean 16 Test seguence for randomness (Runs test) Sample mean Sample mean 17 Custom Custom 18 Mean o Mean 19 eset Cancel 20 OK Cancel Help 21 Go to Settings to activate Windows Variable View Data View IEM SPSS Statistics Processor Is ready 8:31 PM ) ENG 5/16/2019 O Type here to search

As shown above enter data in columns then check assumption of Normality using Non Parametric test

Output1 [Document1]- IBM SPSS Statistics Viewer File Edit View Data Transform Insert Format Analyze Direct Marketing Graphs Utilities Add-ons Window Help EOutput Nonparametric Tests: One Sample Log , Nonparametric Tests NPTESTs /ONESAMPLE TEST (Body_Temperature Brain_Temperatur OLMOGOROV_SMIRNOW (NO Title RMAL SAMPLE) Notes Actve Dataset Model Viewer /MISSING SCOPE-ANALYSIS USERMİSSİNG-EXCLUDE /CRITERIA ALPHA-0.05 C!LEVEL=95 → Nonparametric Tests [DataSet0] Hypothesis Test Summary Null Hypothesis Test Sig Decision The distribution of Body 1 Temperature is normal with mean Kolmogorov- 38.42 and standard deviation 0.17. Smimov Test Retain the 918 null hypothesis One-Sample The distribution of Brain 2 Temperature is normal with mean Kolmogorov 39.06 and standard deviation 0.25. Smimov Test One-Sample Retain the 932 null Asymptotic significances are displayed. The significance level is .05 Activate Windows Go to Settings to activate Windows IBM SPSS Statistics Processor is ready 828 PM ) ENG 5/16/2019 0 Type here to search

As in above output p-value for both variable is > 0.05. Hence we can say that both variable Body and Brain Temperature are Nornally distributed

包.Untitledi DataSetO-IBM SPSS Statistics Data Editor File Edit View Data Transform Anlye Direct Marketing Graphs Utilities Add-ons Window Help LAI Reports 14 Descriptive Statistics Visible: 3 of 3 Variables Tables Ostriches Body Te Compare Means Means.. var var ature General Linear ModelOne-Sample T Test - 38.5 1.00 Generalized Linear Models 㘥Independent-Samples T Test. 2.00 38.4 Mixed Models Paired-Samples T Test. 3.00 38.2 Correlate One-Way ANOVA. 4.00 38.5 Regression 5.00 38.6 38.1 Loglinear 6.00 Neural Networks Classity Dimension Reduction 10 Nonparametric Tests Forecasting 12 Survival 13 Multiple Response 14 15 Missing Value Analysis.. 16 Multiple Imputation 17 Complex Samples 18 Quality Control 19 ROC Curve 20 21 Go to Settings to activate Windows Variable View Data View One-Sample T Test IBM SPSS Statistics Processor is ready 8:31 PM rP ^恤瘺41 ENG 5/16/2019 0 Type here to search
One sample t test for Sample mean under hypothesis
H0 : μ = 38.5V sH1 : μ 38.5

Input test value 38.5 and Run

包"Untitled! [DataSetJ-BM SPSS Statistics Data Editor File Edit View Data Transform Analze Direct Marketing Graphs Utilities Addons Window Help 14 20 Visible: 3 of 3 Variables Ostriches Body_Tempei Brain_Te var var var var var var va ature 39.32 12.003827 38.68 38.51 1.00 38.45 3.00 38.2739.20 400 38.52 3868 5.00 3862 39.09 600 3818 3884 39.21 One-Sample T Test: Options One-Sample T Test Conidence Interval Percentage: 25% 38.84 Test Variable(s) Missing Values Options Ostriches Brain Temperature L Body Temperature Exclude cases analysis by analysis Exclude cases listwise Continue Cancel 10 12 13 Test Value: 38.5 14 OK eset Cancel 15 16 17 18 19 20 21 Go to Settings to activate Windows Variable View Data View IBM SPSs Statistics Processor is ready O Type here to search ) ENG 5/16/2019

As shown above p-value for t test is 0.321 > 0.05. hence we fail to reject null hypothesis

"Output! [Documenti 1-1BM SPSS Statistics Viewer File Edit View Data Transform Insert Format Analyze Direct Marketing Graphs Utilities Add-ons Window Help 曰 包Output Log , Nonparametric Tests Asymptotic significances are displayed. The significance level is .05 Title Notes Active Dataset Model Viewer T-TEST Log ET-Test Tite /TESTVAL=38. 5 MISSING-ANALYSIS Notes VARIABLES-Body_Temperature /CRITERIA-CI (·95) . Active Dataset One-Sample Stati Test T-Test [DataSet0 One-Sample Statistics Std. Error MeanStd. Deviation 38.425016670 Body Temperature 06806 One-Sample Test Test Value 38.5 95% Confidence Interval of the Difference Mean df Sig. (2-tailed Difference Lower Uppe Body Temperature 07500 2499 0999 1.102 321 Activate Windows Go to Settings to activate Windows IBM SPSs Statistics Processor is ready 8:33 PM rP ^恤瘺41 ENG 5/16/2019 O Type here to search

i.e we can say that average body temperature is 38.5

Output1 [Document1]- IBM SPSS Statistics Viewer File Edit View Data Transform Insert Format Analyze Direct Marketing Graphs Utilities Add-ons Window Help E Output Log , Nonparametric Tests Body Temperature Equal vaniances assumed 5.202 63167 12142 90221 36113 1.235 293 Equal variances not assumed 5.202 8.786 12142 35597 001 63167 90736 Active Dataset Model Viewer T-TEST Log T-Test Tite MISSING-ANALYSIS VARIABLEs-Temperature Active Dataset /CRITERIA-CI(.90) One-Sample Stati Test Log T-Test T-Test [DataSet0 Active Dataset One-Sample Statistics One-Sample Test ELog gg T-Test Std. Error MeanStd. Deviation Body Temperature 12 38.7408 38604 11144 Active Dataset Group Statistics 輸Independent Sam One-Sample Test Test Value 0 Log T-Test 90% Confidence Interval of the Difference Mean Sig. (2-tailed Difference Lower Uppe LE Active Dataset @one-Sample Stati 38.74083 Body Temperature 347.638 38.5407 38.9410 Activate Windows Go to Settings to activate Windows IBM SPSS Statistics Processor is ready 8-50 PM 0 Type here to search 5/16/2019

To obtain 90 % confidence interval perform one sample t test with test value 0. The 90 % confidence interval for Body temperature is (38.5407, 38.9410)

b)

To perform Independent sample t test for hypothesis in b we have to enter data as shown above i.e Body and Brain temperature in single column and code Body part as 1 for Body and 2 for Brain

包.Untitledi DataSetO-IBM SPSS Statistics Data Editor File Edit View Data Transform Analye Direct Marketing Graphs Utilities Add-ons Window Help 14 Visible: 3 of 3 Variables Ostriches Temperature Part 38.51 var var var var var var 1.00 1.00 1.00 2.00 38.45 3.00 38.27 1.00 1.00 4.00 38.52 5.00 38.62 1.00 38.18 1.00 6.00 39.32 2.00 39.21 2.00 39.20 2.00 10 38.68 2.00 39.09 2.00 12 38.84 2.00 13 14 15 16 18 19 20 21 23 Go to Settings to activate Windows Variable View Data View IBM SPSs Statistics Processor is ready 8:38 PM ) ENG 5/16/2019 O Type here to search

and declare the Body part variable as Nominal and Enter value 1 for Body and 2 for Brain

包.Untitledi DataSetO-IBM SPSS Statistics Data Editor File Edit View Data Transform Analye Direct Marketing Graphs Utilities Add-ons Window Help Role Measure Miss Values Label Width Decimals Name Input Right Scale None None Numeric Ostriches Scale alInput Input Right None Body Temperat.. None Temperature Numeric Right (1.00, Body. None Part of Body 10 12 13 14 15 16 17 18 19 20 21 23 24 Go to Settings to activate Windows Data View Variable View 旧M SPSS Statistics Processor Is ready 8:39 PM ) ENG 5/16/2019 0 Type here to search

包"Untitled! [DataSetJ-BM SPSS Statistics Data Editor File Edit View Data Transform Analze Direct Marketing Graphs Utilities Addons Window Help 14 Visible: 3 of 3 Variables Ostriches Temperature Partrr ar ar r 1.00 varvar varrar var var 38.51 1.00 2.00 38.45 3.00 3827 4.00 38.52 5.00 38.62 1.00 1.00 1.00 Define Groups Independent-Samples T Test 1.00 6.00 1.00 38.18 oUse specifiedvalues Group 1 1 Test Variable(s) Body Temperature 2.00 39.32 Ostriches 3921 200 39.20 2.00 ap Group 2 2.00 O Cut point 38.68 2.00 10 39.09 2.00 2.00 Continue Cancel 38.84 12 Grouping Variable Part 12) 13 14 Define Groups 15 16 OK 18 19 20 21 23 Go to Settings to activate Windows Variable View Data View IBM SPSs Statistics Processor is ready 8:39 PM O Type here to search 5/16/2019
As shown above perform Independent sample t test to test hypothesis $H0: d =0 Vs H1:d \neq 0$

"Output! [Documenti 1-1BM SPSS Statistics Viewer File Edit View Data Transform Insert Format Analyze Direct Marketing Graphs Utilities Add-ons Window Help 38.42500 38.2501 38.5999 Body Temperature 564.606 曰 包Output Log , Nonparametric Tests T-TEST GROUPS Part (1 2) Title Notes /MISSING-ANALYSIS Active Dataset Model Viewer /VARIABLES Temperature /CRITERIA 1 ( .95) Log T-Test Tite T-Test Notes Active Dataset one-sample Stati Test [DataSet0] Log T-Test Group Statistics Title Std. Error Notes MeanStd. Deviation Active Dataset Body Temperature Body 6 38.4250 6 39.0567 16670 Brain 24631 10055 One-Sample Test ELog 白 T-Test Independent Samples Test Title Levene's Test for Equality of Notes t-test for Equality of Means Variances Active Dataset 95% Confidence Interval ofthe Group Statistics 輸Independent Sam iference Std. Error Mean Sig. (2-tailed) Difference dr Lower Upper Equal variances 12142 36113 Body Temperature 1.235 5.202 63167 90221 assumed 5.202 8.786 Equal variances not 001 12142 63167 90736 35597 assumed Go to Settings to activate Windows IBM SPSs Statistics Processor is ready 840 PM O Type here to search 5/16/2019

The variances are equal as p-value for F test is 0.293 > 0.05.

So we look out for t test with equal variance assume

the p-value for t test is 0.000 < 0.05. Hence we can reject null hypothesis

i.e. There is significant difference in temperature between body and brain