Test the claim that the proportion of men who own cats is larger than 20% at the .005 significance level. The null and alternative hypothesis would be:_.
A. H0: p = 0.2
Ha: p is not equal to 0.2.
B. H0: mu = 0.2
Ha: mu is not equal to 0.2.
C. H0: p = 0.2
Ha: p < 0.2.
D. H0: mu = 0.2
Ha: mu < 0.2
E. H0: mu = 0.2
Ha: mu > 0.2.
The test statistic is:.
The critical value is:.
Based on this we (to 2 decimals) (to 2 decimals):_.
a. reject the null hypothesis.
b. fail to reject the null hypothesis.

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2021-05-22T05:22:26+02:00

Answer:

[tex]C. \\ \\ H_o: p = 0.2 \\ \\ Ha: p < 0.2[/tex]

Step-by-step explanation:

From the given information:

Null & Alternative hypothesis is:

[tex]\ \\ H_o: p = 0.2 \\ \\ Ha: p < 0.2[/tex]

Since the alternative hypothesis is less than 0.2;

Then, the test is left-tailed.

The level of significance ∝ = 0.005

Let assume that:

the sample size n of the people = 55 and there are 19 owned cats;

Then:

Test statistics:

[tex]Z =\dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

[tex]Z =\dfrac{0.19 - 0.2}{\sqrt{\dfrac{0.2(1-0.2)}{55}}}[/tex]

[tex]Z =\dfrac{- 0.01}{\sqrt{\dfrac{0.16}{55}}}[/tex]

[tex]Z =\dfrac{- 0.01}{\sqrt{0.002909}}[/tex]

Z = - 0.18540

Z = - 0.19

At ∝ = 0.005; the critical value [tex]Z_{\alpha/2}= Z_{0.005/2}= -2.58[/tex]

Since the value of the test statistics is greater than the critical value; then, we fail to reject [tex]H_o[/tex] i.e the null hypothesis.