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3 years ago

9

Jillian measured the distance around a small fish pond as 27 yards. Which would be a good estimate for the distance across the p

ond, 14 yards, 9 yards, or 7 yards? Explain how you decided.

1 answer:

Anton [14]3 years ago

8 0

14 because it is half of the width around the pond.

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Answer:

In the graph we can find two points, lets select:

(2, 15) and (4, 30)

Those are the first two points.

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So the slope for our equation is

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now we can find b by imposing that when x = 2, y must be 15 (for the first point we selected)

15 = (15/2)*2 + b = 15 + b

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then our equation is:

y = (15/2)*x

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Gold costs x cents per gram.

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3 years ago

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Answer:

$p_v = P(\chi^2_{29}>42.963)=1-0.954=0.0459$

b. between .025 and .05

Step-by-step explanation:

Previous concepts and notation

The chi-square test is used to check if the standard deviation of a population is equal to a specified value. We can conduct the test "two-sided test or a one-sided test".

$\bar X$ represent the sample mean

n = 30 sample size

s= 0.2 represent the sample deviation

$\sigma_o =\sqrt{0.027}=0.164$ the value that we want to test

$p_v$ represent the p value for the test

t represent the statistic

$\alpha=$ significance level

State the null and alternative hypothesis

On this case we want to check if the population standard deviation is less than 0.027, so the system of hypothesis are:

H0: $\sigma \leq 0.027$

H1: $\sigma >0.027$

In order to check the hypothesis we need to calculate the statistic given by the following formula:

$t=(n-1) [\frac{s}{\sigma_o}]^2$

This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

$t=(30-1) [\frac{0.2}{0.164}]^2 =42.963$

What is the approximate p-value of the test?

The degrees of freedom are given by:

$df=n-1= 30-1=29$

For this case since we have a right tailed test the p value is given by:

$p_v = P(\chi^2_{29}>42.963)=1-0.954=0.0459$

And the best option would be:

b. between .025 and .05

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3 years ago