Full question attached
Answer and explanation:
Null hypothesis : all population proportions are equal, p1=p2=p3=p4
Alternative hypothesis : Not all population proportions are equal
To find our p-value using chi Square method, we first find expected frequencies from observed frequencies above
Expected Frequencies:
Gender A. B. C. D
Male. 46.81 46.81 44.21 43.17
Female 43.19. 43.19 40.79 39.83
Total = 348
chi Square for table = (observed frequency - expected frequency)²/expected frequency
Gender. A. B. C. D
Male. 0.10 0.17 0.52 0.40
Female 0.11 0.18 0.56 0.44
x²= 2.49
Degrees of freedom(df)= k – 1 = (4 – 1) = 3
Using the chi Square table with degree of freedom = 3, 2 and x²= 2.49 shows, the p –value = 0.4771 therefore we do not reject null hypothesis since p value is greater than significance level 0.08
We do not reject the null hypothesis
b. There is no evidence of differences in proportion
