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3 years ago

For khan:) 2x + 5y > -6 - 4x + 3y = 2 Is (-1,7) a solution of the system?

Mathematics

1 answer:

KiRa [710]3 years ago

3 0

Step-by-step explanation:

$let \: 2x + 5y > - 6 ... i \\ - 4x + 3y = 2 ...ii\\ let \: x = - 1 \\ y = 7\\ from \: i \: equation \\ 2x + 5y > - 6 \\ then \: keeping \: value \: of \: x \: and \: y \\ 2 \times - 1 + 5 \times 7 > - 6 \\ - 2 + 35 > - 6 \\ 33 > - 6 \\ from \: ii \: equation \\ - 4x + 3y = 2 \\ - 4 \times - 1 + 3 \times 7 = 2 \\ 4 + 21 = 25$

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At the null hypothesis, it is tested if the proportion is of 0.5, that is:

$H_0: p = 0.5$

At the alternative hypothesis, it is tested if the proportion is different of 0.5, that is:

$H_1: p \neq 0.5$

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}$

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$\overline{p}$ 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:

$p = 0.5, n = 483 + 398 = 881, \overline{p} = \frac{483}{881} = 0.5482$

The value of the test statistic is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}$

$z = \frac{0.5482 - 0.5}{\sqrt{\frac{0.5(0.5)}{881}}}$

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Since we have a two-tailed test(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.

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Since the p-value of the test is 0.0042 < 0.01, 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

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