Respuesta :
Answer:
The claim is true.
Step-by-step explanation:
Given - Suppose a poll is taken that shows that 281 out of 500 randomly selected, independent people believe the rich should pay more taxes than they do.
To find - Test the hypothesis that a majority (more than 50%) believe the rich should pay more taxes than they do. Use a significance level of 0.05.
Solution -
Given that,
X = 281, n = 500
So,
The hypothesis are :
H0 : p = 0.50
H1 : p > 0.50
So,
Sample proportion is
p bar = X/n
     = 281/500
     = 0.562
⇒p bar = 0.562
Now,
Test statistics :
[tex]Z_{0} = \frac{p bar - p}{\sqrt{\frac{p(p - 1)}{n} } } \\= \frac{0.562 - 0.50}{\sqrt{\frac{0.50(0.50 - 1)}{500} } }\\= 0.277[/tex]
∴ we get
[tex]Z_{0} = 0.277[/tex]
SO,
p-value = P( Z ≥ 0.277)
       = 1 - P(Z ≤ 0.277)
       = 1 - 0.997
       = 0.002779
∴ we get
The conclusion is -
As [tex]Z_{0} = 0.277[/tex] > Z = 1.645
We reject H0
And
We have enough information to conclude that the population proportion is greater than 0.50
So,
The claim is true.
