A survey was conducted in the United Kingdom, where respondents were asked if they had a university degree. One question asked, "In the last 20 years the proportion of the world population living in extreme poverty has...", and three choices were provided: 1.)"increased" 2.) "remained more or less the same" and 3.) "decreased". Of 373 university degree holders, 45 responded with the correct decreased; of 639 non-degree respondents, 57 responded with the correct answer1. We would like to test if the percent of correct answers is significantly different between degree holders and non-degree holders. Let group 1 be the degree holders and let group 2 be the non-degree holders.

If we compare the p value and using any significance level for example always so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the two proportions are not statistically different at 5% of significance

Step-by-step explanation:

Data given and notation  

represent the number of correct answers for university degree holders

represent the number of correct answers for university non-degree holders  

sample 1 selected

sample 2 selected

represent the proportion of correct answers for university degree holders  

represent the proportion of correct answers for university non-degree holders  

z would represent the statistic (variable of interest)  

represent the value for the test (variable of interest)

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportions are different between the two groups, 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

Calculate the statistic

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

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 one side test the p value would be:  

If we compare the p value and using any significance level for example always so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the two proportions are not statistically different at 5% of significance