Question

Take your survey data and code the gender question as Male= 0 and Female = 1. Suppose we hypothesize that women are more likely to respond to surveys than men are. Specifically, we believe that more than 55 percent of all respondents are women which equates to the proportion of the gender variable to be greater than 0.55. Test the hypothesis.

Females= 24

Males= 9

Provide the 6 step process of testing the hypothesis.

Present your results and discuss why you rejected or failed to reject the null hypothesis.

Answer 1

Given:

Females= 24

Males= 9

n = 9 + 24 = 33

Sample proportion, ${\hat{p}}$ = X/n = 24/33 = 0.7273

Hypothesis test:

The null and alternative Hypothesis,

Ho : p = 0.55

Ha : p > 0.55 (This is a right - tailed test)

Test statistics:

z = ( ${\hat{p}}$ - p)/√p(1-p)/n

= (0.7273 - 0.55) / √ 0.55(1-0.55)/33

= 2.05

Test statistics is z = 2.05

Rejection Region :
For α = 0.05
Critical value of z is 1.64.

Rreject H0 if z > 1.64.

Since test statistic z = 2.05 > 1.64, we reject null hypothesis.

Using P-value Approach :

P-value = P(z > 2.05 ) = 0.0202
Since P-value < 0.05, we reject null hypothesis.

There is sufficient evidence to conclude the proportion of the gender variable to be greater than 0.55.