Question

Assume two independent random samples are available which provide sample proportions. For the first sample assume n1= 100 and x1= 39. For the second sample, assume n2= 100 and x2= 49. Test the null hypothesis that the population proportions are equal versus the alternative hypothesis that the proportions are not equal at the 90% confidence level. Frame the test statistic by subtracting the proportion for population 1 from that for population 2. Pick an appropriate z value, p-value and conclusion. Round your answer to the nearest thousandth.
a) z-value = -1.425 p-value= 0.077 statistically significant
b) z-value = 1.425 p-value= 0.077 not statistically significant
c) z-value = 1.425 p-value= 0.077 statistically significant
d) z-value = -1.425 p-value= 0.1543 not statistically significant

Answer 1

Answer:a) z-value = -1.425 p-value= 0.077 statistically significant

Step-by-step explanation:

Given the following :

n1 = 100; x1 = 39 ; n2 = 100 ; x2 = 49

Z value for two independent samples can be obtained using the relation :

Z = (p1 - p2) /(√p(1-p)) * (√[(1/n1) + (1/n2)]

Z = -1.425

P-value : using the online p-value calculator at a confidence level of 90% from z score

Obtained p value = 0.077079

The p value is less than 0.1 , hence result is significant at p<0.10