<u>Testing the hypothesis</u>, it is found that since the <u>p-value of the test is 0.0042 < 0.01</u>, it can be concluded that the proportion of subjects who respond in favor is different of 0.5.
At the null hypothesis, it is tested if the <u>proportion is of 0.5</u>, that is:
![H_0: p = 0.5](https://tex.z-dn.net/?f=H_0%3A%20p%20%3D%200.5)
At the alternative hypothesis, it is tested if the <u>proportion is different of 0.5</u>, that is:
![H_1: p \neq 0.5](https://tex.z-dn.net/?f=H_1%3A%20p%20%5Cneq%200.5)
The test statistic is given by:
![z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B%5Coverline%7Bp%7D%20-%20p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281%20-%20p%29%7D%7Bn%7D%7D%7D)
In which:
is the sample proportion.- p is the value tested at the null hypothesis.
- n is the sample size.
In this problem, the parameters are given by:
![p = 0.5, n = 483 + 398 = 881, \overline{p} = \frac{483}{881} = 0.5482](https://tex.z-dn.net/?f=p%20%3D%200.5%2C%20n%20%3D%20483%20%2B%20398%20%3D%20881%2C%20%5Coverline%7Bp%7D%20%3D%20%5Cfrac%7B483%7D%7B881%7D%20%3D%200.5482)
The value of the test statistic is:
![z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B%5Coverline%7Bp%7D%20-%20p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281%20-%20p%29%7D%7Bn%7D%7D%7D)
![z = \frac{0.5482 - 0.5}{\sqrt{\frac{0.5(0.5)}{881}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B0.5482%20-%200.5%7D%7B%5Csqrt%7B%5Cfrac%7B0.5%280.5%29%7D%7B881%7D%7D%7D)
![z = 2.86](https://tex.z-dn.net/?f=z%20%3D%202.86)
Since we have a <u>two-tailed test</u>(test if the proportion is different of a value), the p-value of the test is P(|z| > 2.86), which is 2 multiplied by the p-value of z = -2.86.
Looking at the z-table, z = -2.86 has a p-value of 0.0021.
2(0.0021) = 0.0042
Since the <u>p-value of the test is 0.0042 < 0.01</u>, it can be concluded that the proportion of subjects who respond in favor is different of 0.5.
A similar problem is given at brainly.com/question/24330815