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Sagot :
The p-value of the test hypothesis is: 0.968.
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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
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