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9 months ago

15. Write the slope-intercept form of the line described in the following:Parallel to 4x + 5y=20and passing through (12,4)

Mathematics

1 answer:

Amiraneli [1.4K]9 months ago

3 0

Problem

Write the slope-intercept form of the line described in the following:

Parallel to 4x + 5y=20

and passing through (12,4)

Solution>

For this case we need to have the same slope, and if we write the equation given we see:

5y = 20 -4x

y = 4 -4/5 x

then the slope m = -4/5

and we also know a point given x= 12, y= 4 and we can do the following:

4 = -4/5 (12) +b

4 = -48/5 + b

And if we solve for the intercept we got:

b= 4 +48/5= -28/5

And our equation would be given by:

y = -4/5 x -28/5

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$p_v =P(t_{(63)}>2.5)=0.0075$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean age is significantly higher than 45 years at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=45$ represent the mean height for the sample

$s=16$ represent the sample standard deviation for the sample

$n=64$ sample size

$\mu_o =40$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean age is higher than 40 years, the system of hypothesis would be:

Null hypothesis: $\mu \leq 40$

Alternative hypothesis: $\mu > 40$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{45-40}{\frac{16}{\sqrt{64}}}=2.5$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=64-1=63$

Since is a one right tailed test the p value would be:

$p_v =P(t_{(63)}>2.5)=0.0075$

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