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inna [77]
3 years ago
11

The average size of a new house built in a Hays county in 2010 was 1,872 square feet. A random sample of 40 new homes built in H

ays County were selected in 2014. The average square footage was 2,031 with a standard deviation of 373 square feet. Does this sample provide enough evidence to conclude that the average house size has increased in the Hays County since 2010? Test at an alpha level of 0.05. Find the test statistic.
Mathematics
1 answer:
vlada-n [284]3 years ago
7 0

Answer:

The test statistic is z = 2.7.

The pvalue of the test is 0.0035 < 0.05, which means that this sample provides enough evidence to conclude that the average house size has increased in the Hays County since 2010.

Step-by-step explanation:

The average size of a new house built in a Hays county in 2010 was 1,872 square feet. Evidence that it has increased?

This means that the null hypothesis is:

H_0: \mu = 1872

And the alternate hypothesis is:

H_a: \mu > 1872

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

1872 is tested at the null hypothesis:

This means that \mu = 1872

Sample of 40. The average square footage was 2,031 with a standard deviation of 373 square feet.

This means that n = 40, X = 2031, \sigma = 373

Value of the test-statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{2031 - 1872}{\frac{373}{\sqrt{40}}}

z = 2.7

Pvalue and decision:

The pvalue of the test is the probability of finding a sample mean above 2031. This is 1 subtracted by the pvalue of z = 2.7.

Looking at the z-table, z = 2.7 has a pvalue of 0.9965

1 - 0.9965 = 0.0035

The pvalue of the test is 0.0035 < 0.05, which means that this sample provides enough evidence to conclude that the average house size has increased in the Hays County since 2010.

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13/10+2/100=?/100 do you guys know what it os
Mila [183]

Answer:

132

Step-by-step explanation:

13/10+2/100=?/100

Get a common denominator of 100 for the first term

13/10  * (10/10)  +2/100=?/100

130/100 + 2/100 = ?/100

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4 0
2 years ago
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use the elimination method to solve the system of equations. choose the correct ordered pair x+y=3 y=8
klasskru [66]

Answer:

(-5, 8)

Step-by-step explanation:

Step 1: Multiply 2nd equation by -1

x + y = 3

-y = -8

Step 2: Elimination

x = -5

Step 3: Find <em>y</em>

y = 8

7 0
2 years ago
I need the whole solution
ddd [48]

Confused what the question is. Are you looking for the product or the zeroes?

If you are looking for the product, then:

Use foil to get: sec²(1) - sec²(-csc²) -1(1) -1(-csc²)

= sec² + sec²csc² - 1 + csc²

= sec²csc² + sec² + csc² - 1

= sec²csc² + 1 - 1 (NOTE: sec² + csc² = 1 is an identity)

= sec²csc²

Answer: sec²csc²

***************************************************

If you are looking for the zeroes, then:

Using the zero product property, set each factor equal to zero and solve.

<u>First factor:</u>

sec²Θ - 1 = 0

sec²Θ = 1

secΘ = 1, -1

remember that secΘ is \frac{1}{cos}

\frac{1}{cos} = 1 \frac{1}{cos} = -1

cross multiply to get:

cosΘ = 1 cosΘ = -1

use the unit circle (or a calculator) to find that Θ = 0 and π

<u>Second factor:</u>

1 - csc²Θ = 0

1 = csc²Θ

1, -1 = cscΘ

remember that cscΘ is \frac{1}{sin}

\frac{1}{sin} = 1 \frac{1}{sin} = -1

cross multiply to get:

sinΘ = 1 sinΘ = -1

use the unit circle (or a calculator) to find that Θ = \frac{\pi}{2} and \frac{3\pi}{2}

Answer: 0, π, \frac{\pi}{2} , \frac{3\pi}{2}

7 0
3 years ago
Problems 40-45 I need assistance with​
Greeley [361]

40. Multiply each row in the first matrix by each column in the second matrix.

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41. E. Matrix

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Vilka [71]

Answer:

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Step-by-step explanation:

now first in order to count we will have to turn 3 1/4 into a whole number which means we will have to multiply the denomintor by 3 and add it to the numerator which is 1

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13/4  and the denominator always stays the same

and now to count we will have to divide 13/4 divided by 1/4

now instead of dividing you can just multiply them by switching the denominator and numerator  1/4  to  4/1  

13/4 x 4/1

52/4

13


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3 years ago
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