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3 years ago

Slope intercept equation for (0,-4) and (4,1)

Mathematics

1 answer:

Fudgin [204]3 years ago

8 0

Answer:

y = (5/4)x - 4

Step-by-step explanation:

As we move from (0, -4) to (4, 1), x increases by 4 and y increases by 5.

Thus, the slope of the line segment connecting these two points is

m = rise / run = 5/4.

Subbing these knowns into the point-slope formula for the equation of a straight line, we get:

y - 1 = (5/4)(x - 4), or

y = (5/4)x - 5 + 1, or

y = (5/4)x - 4

Let's check this out. Determine whether or not (0, -4) satisfies the equation:

-4 = (5/4)(0) - 4

Yes, this is true; the equation is correct.

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Answer:

a) Null hypothesis: $\mu \leq 120$

Alternative hypothesis: $\mu > 120$

b) $t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236$

The degrees of freedom are given by:

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The p value for this case taking in count the alternative hypothesis would be:

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Step-by-step explanation:

Information given

$\bar X=130$ represent the sample mean for the amount spent each shopper

$s=40$ represent the sample standard deviation

$n=80$ sample size

$\mu_o =120$ represent the value to verify

t would represent the statistic

$p_v$ represent the p value f

Part a

We want to verify if the shoppers participating in the loyalty program spent more on average than typical shoppers, the system of hypothesis would be:

Null hypothesis: $\mu \leq 120$

Alternative hypothesis: $\mu > 120$

The statistic for this case would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236$

The degrees of freedom are given by:

$df = n-1 = 80-1=79$

The p value for this case taking in count the alternative hypothesis would be:

$p_v =P(t_{79}>2.236)=0.0141$

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