Arandom sample of n 1n1equals=139139 individuals results in x 1x1equals=3737 successes. an independent sample of n 2n2equals=147147 individuals results in x 2x2equals=5858 successes. does this represent sufficient evidence to conclude that p 1 less than p 2p1

If we compare the p value and using any significance level for example we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significant lower than the proportion 2 at 5% of significance.  

Step-by-step explanation:

1) Data given and notation  

represent the number of people with characteristic 1

represent the number of people with characteristic 2

sample 1 selected

sample 2 selected

represent the proportion of people with characteristic 1

represent the proportion of people with characteristic 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 less than the 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 we can assuem it 0.05, and we can calculate the p value for this test.  

Since is a one left tailed test the p value would be:  

So if we compare the p value and using any significance level for example we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significant lower than the proportion 2 at 5% of significance.  

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step-by-step explanation:

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