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nasty-shy [4]
3 years ago
11

The standard deviation of math test scores at one high school is 16.1. A teacher claims that the standard deviation of the girls

' test scores is smaller than 16.1. A random sample of 22 girls results in scores with a standard deviation of 12.9. Use a significance level of 0.01 to test the teacher's claim.
Mathematics
1 answer:
Elanso [62]3 years ago
3 0

Answer:

\chi^2 =\frac{22-1}{259.21} 166.41 =13.482

p_v =P(\chi^2

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(13.482,21,TRUE)"

If we compare the p value and the significance level provided we see that p_v >\alpha so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population deviation is not significantly lower than 16.1 at 1% of significance.

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

n=22 represent the sample size

\alpha=0.01 represent the confidence level  

s^2 =12.9^2=166.41 represent the sample variance obtained

\sigma^2_0 =16.1^2 =259.21 represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population deviation is smaller than 16.1 (that's equivalent to check if the population variance is lower than 259.21:

Null Hypothesis: \sigma^2 \geq 259.21

Alternative hypothesis: \sigma^2

Calculate the statistic  

For this test we can use the following statistic:

\chi^2 =\frac{n-1}{\sigma^2_0} s^2

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

\chi^2 =\frac{22-1}{259.21} 166.41 =13.482

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 21. And since is a left tailed test the p value would be given by:

p_v =P(\chi^2

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(13.482,21,TRUE)"

Conclusion

If we compare the p value and the significance level provided we see that p_v >\alpha so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population deviation is not significantly lower than 16.1 at 1% of significance.

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Answer:

Deductive Reasoning

Step-by-step explanation:

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we also take

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So if Rover is a dog, and all dogs in the kennel are collies, then Rover is a collie, because he is a dog and inside the kennel (after we take the statement all dogs in the kennel are collies).

This type of reasoning follows the Deductive Reasoning pattern, if A = B, and B is C then A is also C.

While inductive takes that if A = B, and C is B just like D is B, then E is also B.

6 0
3 years ago
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as
const2013 [10]
<h2>Answer:</h2>

a. True.

b. False.

c. True.

d. True.

e. True.

<h2>Step-by-step explanation:</h2>

a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.

b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.

c. This statement is true because angles 5 and 1 correspond to each other.

d. This statement is true because angles 7 and 8 form a straight line.

e. This statement is true because they are interior angles that are alternate.

<h3>Hope this helps! </h3>

8 0
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41,620,000 is the answer
5 0
3 years ago
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A population of 1,000 squirrels lives on a rectangle-shaped farm plot that is 25 feet long by 10 feet wide what is the populatio
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5 0
3 years ago
I cant figure this one out at all
eduard

Answer:

a. 2^(x-2) = g^(-1)(x)

b. A, B, D

Step-by-step explanation:

the phrasing attached in the image is flagged as inappropriate, so i will be replacing it with g(x) and its inverse with g^(-1)(x)

1. replace g(x) with y and solve for x

y = log₂(x) + 2

subtract 2 from both sides to isolate the x and its log

y - 2 = log₂(x)

this text is replaced by the second image -- it was marked as inappropriate

thus, 2^(y-2) = x

replace x with g^(-1)(x) and y with x

2^(x-2) = g^(-1)(x)

2. plug this in to points A, B, C, D, E, and F

A: (2,1)

plug 2 in for x

2^(2-2) = 2⁰ = 1 so this works

B: (4, 4)

2^(4-2) = 2²= 4 so this works

C: (9, 3)

2^(9-2) = 2⁷ = 128 ≠ 3 so this doesn't work

(5, 8)

2^(5-2) = 2³ = 8 so this works

E: (3, 5)

2^(3-2) = 2¹ = 2 ≠ 5 so this doesn't work

F: (8, 5)

2^(8-2) = 2⁶ = 64 ≠ 5 so this doesn't work

4 0
2 years ago
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