Answer:
Since is a two tailed 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 reject the null hypothesis, and we can say the two proportions are significantly different.
Step-by-step explanation:
Data given and notation
represent the number of men with cats
represent the number of women with cats
sample for men
sample for women
represent the proportion of men with cats
represent the proportion of women with cats
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, 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 two tailed 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 reject the null hypothesis, and we can say the two proportions are significantly different.