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4 years ago

6

Write an equation in slope -intercept form for a line that passes through (-2,7) and (14,21)

1 answer:

Georgia [21]4 years ago

7 0

(-2,7) and (14,21)

Find the slope by using the formula $m = \frac{y2 - y1}{x2 - x1}$

Plug in the numbers. $m = \frac{21 - 7}{14 - - 2} 
 \\ m= \frac{14}{16} = \frac{7}{8} 
$

Write it in point slope form first

y - y1 = m(x - x1)
y - 7 = 7/8(x - -2)
y - 7 = 7/8x + 1.75
+ 7 +7

y = 7/8x + 8.75

Our final equation would be: <span>y = 7/8x + 8.75</span>

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Using the t-distribution, it is found that since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

At the null hypothesis, we <u>test if the groups have the same values</u>, that is, the subtraction of their means is 0:

$H_0: \mu_2 - \mu_1 = 0$

At the alternative hypothesis, we <u>test if the groups have different values</u>, that is, the subtraction of their means is different of 0:

$H_1: \mu_2 - \mu_1 \neq 0$

First, we have to find the mean and the standard deviation for both samples, hence, using a calculator:

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The standard errors are:

$s_1 = \frac{\sigma_1}{\sqrt{n_1}} = \frac{6.2507}{\sqrt{8}} = 2.21$

$s_2 = \frac{\sigma_2}{\sqrt{n_2}} = \frac{4.2678}{\sqrt{8}} = 1.5089$

For the distribution of differences, we have that:

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$t = \frac{\overline{x} - \mu}{s}$

In which $\mu$ is the value tested at the null hypothesis, which is 0 for this problem. Hence, the value of the test statistic is:

$t = \frac{\overline{x} - \mu}{s}$

$t = \frac{1 - 0}{2.676}$

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Using a t-distribution calculator, this p-value is of 0.72.

Since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

A similar problem is given at brainly.com/question/15682365

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