A study was performed to examine the personal goals of children in graders 4,5 a

Question

A study was performed to examine the personal goals of children in graders 4,5 and 6. A random sample of students was selected for each of the grades 4,5 and 6 from schools in Georgia. The students received a questionnaire regarding achievement of personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. results are below.

1) Which hypotheses are being tested by the chi-square test of the above data?

a) The null hypothesis is that the mean personal goal is the same for boys and girls, and the alternative is that the means differ.

b) The null hypothesis is that personal goals and gender are independent, and the alternative is that they are dependent.

c) The distribution of gender is differnet for the three different personal goals.

d) The distribution of personal goals is different for boys and girls.

2) The chi-square statistic is (give your answer to 2 decimal places)

3) Based on the chi-square test, we:

a) Reject the null hypothesis at both alpha =5% and alpha =1%

b) fail to reject the null hypothesis at both alpha =5% and alpha =1%

c) reject the null hypothesis at alpha =5%, but fail to reject the null hypothesis at alpha =1%

d) fail to reject the null hypothesis at alpha =5%, but reject the null hypothesis at alpha =1%

Explanation / Answer

1)
b) The null hypothesis is that personal goals and gender are independent, and the alternative is that they are dependent.

2)
TS = 89.96616001

3)
p-value = 0.0000 < 0.05 or < 0.01
A) Reject the null hypothesis at both alpha =5% and alpha =1%

Please rate

c1 c2 c3 sum r1 96 32 94 222 r2 295 45 40 380 sum 391 77 134 602 Eij 1 2 3 expected 1 144.1894 28.39535 49.41528 2 246.8106 48.60465 84.58472 0i 96 32 94 295 45 40 Ei 144.1894 28.39535 49.41528 246.8106 48.60465 84.584718 sum (Oi-Ei)^2/Ei 16.10532 0.457593 40.22636 9.408895 0.267331 23.500664 89.96616 critical value 5.991465 p-value 2.91E-20

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