Let n1equals50, upper x 1equals30, n2equals50, and upper x 2equals10. complete parts (a) and (b) below. a. at the 0.05 level of significance, is there evidence of a significant difference between the two population proportions? determine the null and alternative hypotheses. choose the correct answer below. a. upper h 0 : pi 1 equals pi 2 upper h 1 : pi 1 not equals pi 2 your answer is correct. b. upper h 0 : pi 1 greater than or equals pi 2 upper h 1 : pi 1 less than pi 2 c. upper h 0 : pi 1 less than or equals pi 2 upper h 1 : pi 1 greater than pi 2 d. upper h 0 : pi 1 not equals pi 2 upper h 1 : pi 1 equals pi 2 calculate the test statistic, upper z subscript stat, based on the difference p1minusp2.

Null hypothesis:  

Alternative hypothesis:  

So the p value is a very low value and using any significance level for example always so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.

Step-by-step explanation:

1) Data given and notation  

represent the number of people with a characteristic in 1

represent the number of people with a characteristic in 2

sample of 1 selected  

sample of 2 selected  

represent the proportion of people with a characteristic in 1

represent the proportion of people with a characteristic in 2

z would represent the statistic (variable of interest)  

represent the value for the test (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion 1 is different from proportion 2 , the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

We need to apply a z test to compare proportions, and the statistic is given by:  

  (1)  

Where  

3) Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

4) Statistical decision

For this case we don't have a significance level provided , but we can calculate the p value for this test.    

Since is a two sided test the p value would be:  

So the p value is a very low value and using any significance level for example always so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.