This problem is from Groebner et al, 9th edition Bus. Stat. one of the survey in

Question

This problem is from Groebner et al, 9th edition Bus. Stat.

one of the survey indicates 56% of women have experience with GOS device. The survey indicates 66% of the men surveyed have used GPS.

a. If the survey was based on a sample size of 200 men, do these data indicate that the proportion of men is the same as the proportion of women? use significane level 0.05

b. Obtain the p-value for the test indicated in part a.

What's the survey of women's proportion to do with this problem? This exercise is under the chapter of estimating the proportion of single population.

Thanks for your help!

Explanation / Answer

Given size of men’s sample survey = n = 200. The observed proportion of men having experience of GPS = 0.66.

Set up the hypothesis as follows;

H0 : Pm = 0.56 Vs HA : Pm > 0.56

The test statistic under H0 is

Z = (Sample Proportion (p) – Specified Proportion (P))/(P*Q/n) ~ N(0,1) where Q = 1-P

Z = (0.66-0.56)/(0.56*0.44/200) = 2.849014 > 1.644854 Z Table value for 0.05.

Hence the hypothesis H0 is rejected.

P-value of the test = 0.002193

This exercise indicates that proportion of men having experience of GPS is more than that of women.    

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