Respuesta :
Answer:
The null hypothesis was not rejected.
The proportion of readers who own a personal computer is 47%.
Step-by-step explanation:
The claim made by a publisher is that 47% of their readers own a personal computer.
A single proportion z-test can be used to determine whether the claim made by the publisher is authentic or not.
The hypothesis for this test can be defined as follows:
H₀: The proportion of readers who own a personal computer is 47%, i.e. p = 0.47.
Hₐ: The proportion of readers who own a personal computer is different from 47%, i.e. p ≠ 0.47.
The information provided is:
[tex]n=280\\\hat p=0.43\\\alpha =0.01[/tex]
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.43-0.47}{\sqrt{\frac{0.47(1-0.47)}{280}}}=-1.34[/tex]
The test statistic value is, z = -1.34.
Decision rule:
If the p-value of the test is less than the significance level α = 0.01 then the null hypothesis will be rejected and vice-versa.
Compute the p-value as follows:
[tex]p-value=2\times P (Z < z)[/tex]
[tex]=2\times P (Z < -1.34)\\=2\times [1-P(Z<1.34)]\\=2\times [1-0.90988]\\=0.18024\\\approx0.18[/tex]
*Use a z table for the probability.
The p-value of the test is 0.18.
p-value = 0.18 > α = 0.01
The null hypothesis was failed to be rejected at 1% level of significance.
Conclusion:
There is enough evidence to support the claim made by the publisher. Hence, it can be concluded that the proportion of readers who own a personal computer is 47%.
