study was conducted in which the students from a random sample of 24 high school

Question

study was conducted in which the students from a random sample of 24 high school students were each asked to give r grade point average (GPA). The block design below shows the GPAs of male and female students from four different age groups. Use a technology tool and the block design to perform a two way ANOVA test. Use -0.5. Interpret the results Gender Under 15 17 18 Over 18 Male 2.9,3.2,38 26, 1.4, 1.7 3.2, 24, 18 2.9, 3,1,3.6 Female 3.7,2.5, 2.1 28,3.0,16 2.7.22,15 2.7,3.4,3.7 Determine the null and alternative hypotheses for the main effects. Select all that apply. A. Ho: Age has no effect on Gender. Ha: Age has an effect on Gender C. Ho: Gender has no effect on GPA. Ha: Gender has an effect on GPA E. Ho: Gender has no effect on Age. Ha: Gender has an effect on Age B. Ho: GPA has no effect on Age. Ha: GPA has an effect on Age. D. Ho: Age has no effect on GPA Ha: Age has an effect on GPA. F. Ho: GPA has no effect on Gender Ha: GPA has an effect on Gender Determine the null and alternative hypothesis for the interaction effect. Chcose the correct answer below. O A. Ho. The interaction between ?. ??. The interaction between O c. Ho: The interaction between Gender and GPA has no effect on Age GPA and Age has no effect on Gender Age and Gender has no effect on GPA Ha: There is an interaction effect between Gender and GPA on Age. Ha: There is an interaction effect between GPA and Age on Gender Ha: There is an interaction effect between Age and Gender on GPA Determine the test statistics for the main effects. Select the correct choice below, and, if necessary, fill in any answer boxes to complete your choice. (Round to two decimal places as needed.) OA. The test statistic for the main effect of Age on GPA is The test statistic for the main effect of Gender on GPA is The test statistic for the main effect of GPA on Age is The test statistic for the main effect of Gender on Age is The test statistic for the main effect of Age on Gender is The test statistic for the main effect of GPA on Gender is B. ° C. Determine the test statistic for the the interaction effect. (Round to two decimal places as needed.) Determine the P-value for the main effects. Select the correct choice below, and, if necessary, fill in any answer boxes to complete your choice. Round to three decimal places as needed.) 0 A. The P-value for the main effect of Age on Gender is The Pevalue for the main effet f GPA on Genderis The Paralue for the mai effect of Gcander on GPA S O B. The P-value for the main effect of Age on GPA is

Explanation / Answer

(first part) C and D

(second part) C

(third part) B.

test statistic for main effect of age on GPA=4.22

test statistic for main effect of gender on GPA=0.05

test statistic for interaction F=0.91

(fourth part)

p-value for main effect of age on GPA=0.022

p-value for main effect of gender on GPA=0.822

p-value for interaction p=0.459

(fifth part) B. reject the null hypothesis for one of the main effect only

(sixth part) I and L

(seventh part)D. the interaction between age and gender has no effect on GPA

following informations have been generated from the given data

Source DF Sum of Squares Mean Square F P Model 7 6.01292 0.85899 2.2 0.0902 Error 16 6.23333 0.38958 Total 23 12.2463 Source DF Anova SS Mean Square F P Genger(G) 1 0.02042 0.02042 0.05 0.8218 Age(A) 3 4.93125 1.64375 4.22 0.0223 Interaction G*A 3 1.06125 0.35375 0.91 0.459

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