Question

Answer all questions using R statistical software. Print all R codes and relevant R output. Include the hypotheses, conclusion and interpretation of all tests where necessary.

In a group of 83 persons, there are 42 males and 41 females. Among the 42 males, 32 has brown eyes and among the 41 females, 36 has brown eyes. Let be the proportion of males with brown coloured eyes and the proportion of females with brown coloured eyes.

At α = 0.05, state and test the hypothesis that there is no significant difference in the proportion of males and females with brown eyes in the group of persons. Calculate the test statistic and appropriate p-value.

If we use α = 0.10 level of significance, will the test results be the same?   

Answer 1

x1 = 32

n1 = 42

x2 = 36

n2 = 41

Claim: There is no significant difference in the proportion of males and females with brown eyes in a group of persons.

The null and alternative hypothesis is:

HO: P1 = P2

H1: P1 + P2

R codes and output:

prop.test(x=c(32,36),n=c(42,41),correct=FALSE)

   2-sample test for equality of proportions without continuity
   correction

data: c(32, 36) out of c(42, 41)
X-squared = 1.8902, df = 1, p-value = 0.1692
alternative hypothesis: two.sided
95 percent confidence interval:
-0.27931469 0.04702665
sample estimates:
prop 1 prop 2
0.7619048 0.8780488

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P-value = 0.1692

P-value > 0.05 we fail to reject null hypothesis.

Conclusion:

There is no significant difference in the proportion of males and females with brown eyes in a group of persons.

If we use α = 0.10 level of significance.

P-value > 0.10 we fail to reject null hypothesis.

Conclusion:

There is no significant difference in the proportion of males and females with brown eyes in a group of persons.