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 (this equates to the proportion of the gender variable to be greater than 0.55). Use the methods learned this week to test this hypothesis.

Females= 27 Males= 8

Make sure you go through the 5-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= 27 = x

Males= 8

Total number of respondents = n = 27 + 8 = 35

Sample proportion, = x / n = 27 /35 = 0.7714

Hypothesis test:

The null and alternative Hypothesis,

Ho : p = 0.55

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

Test statistics:

z = ( - p ) /

= (0.7714 - 0.55) /

= 2.633

Test statistics is z = 2.633

P - value = 0.00427 (using z table)

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

Reject H₀  if P -value <
0.00427 < 0.05, we reject null hypothesis.

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

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