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3 years ago

35 POINTS FOR CORRECT ANSWER! write the equation of the line in slope-intercept form. (image attached).

Mathematics

1 answer:

Masteriza [31]3 years ago

4 0

Let's find 2 decipherable points on the graph.
1. (0, 4)
2. (4, 0)

Now, solve for slope.
Slope formula: $\frac{y2-y1}{x2-x1}$
Plug in and solve: $\frac{0-4}{4-0} = \frac{-4}{4} = -1$
Slope: $-1$

Finally, plug into point-slope formula and solve for slope-intercept.
Point-slope formula: $y - y1 = m(x - x1)$ where m = slope
Plug in and solve for slope-intercept.
$y - 4 = -1(x - 0) 

y - 4 = -1x + 0 

Add 4 both sides

y = -1x + 4$
Answer: $y = -x + 4$

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The null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0$

being the subindex 1 for the experimental group and subindex 2 for the control group.

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Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the vaccine was effective.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0$

The significance level is 0.01.

The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.

$p_1=X_1/n_1=21/100000=0.0002$

The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.

$p_2=X_2/n_2=30/100000=0.0003$

The difference between proportions is (p1-p2)=-0.0001.

$p_d=p_1-p_2=0.0002-0.0003=-0.0001$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026$

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$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26$

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

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The null hypothesis failed to be rejected.

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