Answer:
We need to conduct a hypothesis in order to check if that the proportion of men who own cats is significantly different than the proportion of women who own cats , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
And the best option would be:
h 0 : p m = p f h 1 : p m ≠ p f
So the p value is a very high value and using any significance level for example we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis
Step-by-step explanation:
Data given and notation
sample of male selected
sample of female selected
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 that the proportion of men who own cats is significantly different than the proportion of women who own cats , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
And the best option would be:
h 0 : p m = p f h 1 : p m ≠ p f
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
Statistical decision
The significance level provided is , 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 high value and using any significance level for example we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis