SOLUTION: Can someone please check my work and help me understand c,d,e? I figured out the answers by following the formulas but I am not sure why. Chi-square test of independence Diploma

Question 1048522: Can someone please check my work and help me understand c,d,e? I figured out the answers by following the formulas but I am not sure why.
Chi-square test of independence
Diploma-- No Diploma-- Total
Male: 56-- 32-- 88
Female: 62-- 41-- 103
Total: 118-- 73-- 191
a.Have the assumptions for this test been met? Why or why not?
Yes, because Yes E ≥ 5
b.State the null and alternative hypotheses for this test.
H0 : There is not a relationship between gender and whether or not someone is a college graduate (they are independent).
Ha: There is a relationship between gender and whether or not someone is a college graduate (they are dependent).
c. Calculate the test statistic for this test. Explain what is the test statistic represents.
The test statistic is 0.2381
d. What is the p-value? Explain what this p-value represents
The p-value is .625559
e. What is the conclusion for this test at the 0.05 level of significance. Are these variables dependent/associated? Why or why not?
p < .05 The data provides sufficient evidence, at the 0.05 level of significance, that the variables are independent.
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Diploma-- No Diploma-- Total
Male: 56-- 32-- 88
Female: 62-- 41-- 103
Total: 118-- 73-- 191
c.Apply Chi-square test for Independence
(using the chi-square test for independence to determine whether gender is related to getting a diploma)
E1,1 = (88 * 118) / 191 = 54.4, E1,2 = (88 * 73) / 191 = 33.6
E2,1 = (103 * 118) / 191 = 63.6, E2,2 = (103 * 73) / 191 = 39.4
X^2 = (56- 54.4)^2/54.4 + (32- 33.6)^2/33.6 + + (62 -63.6)^2/63.6 + (41 - 39.4)^2/39.4
x^2 = .2282 = .23
d. p-value is used to access the probability of X^2 having 1 degree of freedom is more extreme than .23
DF is (r - 1) * (c - 1) = (2 - 1) * (2 - 1) = 1 (two rows, 2 columns)
P(X^2 > .23) = 1 - .37 = .63
e. 0.05 level of significance
.63 > .05, accept Ho
whether or not someone is a college graduate is not related to gender(they are independent).

a. Yes, random sampling, categorical variables and expected frequency counts > 5
|
b.
Ho : There is not a relationship between gender and whether or not someone is a college graduate (they are independent).
Ha: There is a relationship between gender and whether or not someone is a college graduate (they are dependent).
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