Respuesta :
Answer:
The null and alternate hypothesis would be
H0: pm = pf
H1: pm < pf
Test is left tailed
The test statistic: z = -0.98
The p-value: 0.1365
We fail to reject the null hypothesis
Conclusion: There is not enough evidence to support the claim that the proportion of men who own cats is less than the proportion of women who own cats
Step-by-step explanation:
The null and alternate hypothesis would be
H0: pm = pf
Ha: pm < pf
because they say that the test claim is the proportion of men is smaller less than the proportion of women. The null hypothesis always get the statement of equality (the equals sign). In this case, the alternate hypothesis is the claim.
The test is left tailed because the alternate hypothesis has a < sign. It's strictly less than a value, so it's one tailed, and the < or > sign points to the area of rejection, so in this case, it's pointing left
The test statistic is calculation is attached as a photo
The p-value is found by looking it up on the chart using z = -0.98
Since 0.1365 > 0.005, we fail to reject the null hypothesis
Because we fail to reject the null, there is not enough evidence to support the claim
Answer:
There is not enough evidence to support the claim that the proportion of man who owns the cat is less than the proportion of women who owns the cat.
Hence, the Null and Alternate hypothesis would be
[tex]H_0: p_m=p_f\\H_1=p_m<p_f\\[/tex]
Step-by-step explanation:
Given information:
The test claims that the proportion of men who owns cat is smaller
The significance level = 0.005
As the null hypothesis always gets ten statement of equality but in the case given alternate hypothesis will claim.
Now calculate the Z-value from the given data.
[tex]p=(10+14)/(80)\\p=0.3\\[/tex]
So,
[tex]Z=\frac{p_1-p_2}{\sqrt{p'(1-p')(\frac{1}{n_1}+\frac{1}{n_2}) } }[/tex]
On putting the values in above equation :
[tex]z=\frac{0.25-0.35}{0.3\times 0.7\times 0.2}[/tex]
[tex]z=-0.975[/tex]
The p-value according to the obtained Z value is 0.1365
Since , 0.1365>0.005, we fail to reject null hypothesis.
hence, There is not enough evidence to support the claim that the proportion of man who owns the cat is less than the proportion of women who owns the cat.
Hence the Null and Alternate hypothesis would be
[tex]H_0: p_m=p_f\\H_1=p_m<p_f\\[/tex]
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