Question

it is reported that the percentage of males 18 and older who have never been married is greater than the percentage of females 18 and over who have never been married. in a particular county, out of 50 males surveyed, 32% had never been married. while out of 40 females, 25% had never been married. conduct a hypothesis to determine if the proportion of men is greater than the proportion of women. let confidence level=0.05. use the p-value method.

Answer 1

p1 : Proportion of males 18 and older who have never been married

p2 : Proportion of females 18 and older who have never been married

Null hypothesis : Ho: p1-p2 = 0

Alternative hypothesis : H1 :  p1-p2 > 0 (p1 > p2)

Right tailed test:

Male Sample :

Number of males surveyed : Sample size of male : n1 = 50

Sample proportion of male 18 and older who have never been married : = 32/100 =0.32

Female sample :

Number of females surveyed : Sample size of male : n2 = 40

Sample proportion of female 18 and older who have never been married : = 25/100 =0.25

Method 1 : Individual proportions

p-value for right tailed test :

p-value = 0.2308

=0.05

As p-value is greater than level of significance: i.e (p-value:0.2308 > 0.05:); Fail to Reject Null Hypothesis.

There is not sufficient evidence to conclude that the proportion of men is greater than the proportion of women

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.Method 2 : pooled proportions

p-value for right tailed test :

p-value = 0.2333

=0.05

As p-value is greater than level of significance: i.e (p-value:0.2333 > 0.05:); Fail to Reject Null Hypothesis.

There is not sufficient evidence to conclude that the proportion of men is greater than the proportion of women