Engage with knowledgeable experts and get accurate answers on IDNLearn.com. Our community provides accurate and timely answers to help you understand and solve any issue.
Sagot :
The p-value of the test hypothesis is: 0.968.
-----------------------
At the null hypothesis, we test that the proportions are equal, that is:
[tex]p_1 = p_2 \rightarrow p_1 - p_2 = 0[/tex]
At the alternative hypothesis, we test that the proportions are different, that is:
[tex]p_1 - p_2 \neq 0[/tex]
The test statistic is:
[tex]Z = \frac{X - \mu}{s}[/tex]
In which:
- X is the difference of the two proportions.
- [tex]\mu[/tex] is the value tested at the hypothesis.
- s is the standard error of the difference of the proportions.
The proportions are:
[tex]p_1 = \frac{48}{3000} = 0.016[/tex]
[tex]p_2 = \frac{46}{3000} = 0.0153[/tex]
The parameters are:
[tex]X = p_1 - p_2 = 0.016 - 0.0153 = 0.0007 [/tex]
[tex]s = \sqrt{p_1^2 + p_2^2} = \sqrt{0.0016^2 + 0.0153^2} = 0.0154[/tex]
- 0 is tested at the hypothesis, thus [tex]\mu = 0[/tex]
The value of the test statistic is:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.0007 - 0}{0.0154}[/tex]
[tex]Z = 0.04[/tex]
We are testing if the proportions are different, thus the p-value is P(|Z| > 0.04).
- Looking at the z-table, Z = -0.04 has a p-value of 0.484.
- 2 x 0.484 = 0.968
The p-value is of 0.968.
A similar problem is given at https://brainly.com/question/24350184
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.
