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3 years ago

10. Given Triangle GHI with G(7, 0), H (-5, 5) and I (1, 9), find the slope of HI.

Mathematics

1 answer:

Y_Kistochka [10]3 years ago

3 0

H = (-5,5)
I = (1,9)

slope formula : (y2 - y1) / (x2 - x1)
slope = (9 - 5) / (1 - (-5) = 4 / (1 + 5) = 4/6 reduces to 2/3 <==

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Null hypothesis:

$H_0: \sigma^2 = \sigma_0^2$

Alternative hypothesis:

$H_1: \sigma^2 \neq \sigma_0^2$

The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.

$X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}$

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$X_0^2 = \dfrac{(27)(160.0225)}{132.9409}$

$X_0^2 = \dfrac{4320.6075}{132.9409}$

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$X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}$

From the chi-square probabilities table at 0.975 and degree of freedom 27;

$X^2_{0.975 , 27}$ = 14.573

$X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}$

$X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}$

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$X^2_{0.025 , 27}=$ 43.195

Decision Rule: To reject the null hypothesis if $X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}$ ; otherwise , do not reject the null hypothesis: