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Sladkaya [172]
1 year ago
13

A random sample of 40 binomial trials resulted in 14 successes. test the claim that the population proportion of successes does

not equal 0.50. use a level of significance of 0.05.
Mathematics
1 answer:
mylen [45]1 year ago
5 0

Using the z-distribution, since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

<h3>What are the hypotheses tested?</h3>

At the null hypotheses, we test if the proportion of successes equals 0.5, hence:

H_0: p = 0.5

At the alternative hypotheses, we test if it does not equal, hence:

H_1: p \neq 0.5

<h3>What is the test statistic?</h3>

The test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

In which:

  • \overline{p} is the sample proportion.
  • p is the proportion tested at the null hypothesis.
  • n is the sample size.

For this problem, the parameters are given by:

n = 40, \overline{p} = \frac{14}{40} = 0.35, p = 0.5

Hence the test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

z = (0.35 - 0.5)/(0.5/sqrt(40))

z = -1.9.

<h3>What is the decision?</h3>

Using a z-distribution calculator, considering a two-tailed test, as we are testing if the proportion is different of a value, with z = -1.9, we get that the p-value of the test is of 0.057.

Since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

More can be learned about the z-distribution at brainly.com/question/16313918

#SPJ4

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5. When looking at a map, a student realizes that Birmingham is nearly due west of Atlanta, and Nashville is nearly due north of
leonid [27]

Answer: 250 mi

Step-by-step explanation:

Here we can think in a triangle rectangle:

The distance from Birmingham to Atlanta is roughly 150 mi, and this is one of the cathetus.

And the distance from Birmingham to Nashville is roughly 200 mi, this is the other cathetus of the triangle.

Now, the distance from Atlanta to Nashville will be the hypotenuse of this triangle rectangle.

Now we can apply the Pythagorean's theorem:

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse:

Then:

H = √(A^2 + B^2)

H = √(150^2 + 200^2) mi = √(62,500) mi = 250 mi

Then the estimated distance from Atlanta to Nashville is 250 mi

6 0
3 years ago
Solve the proportional<br> equation below:<br> x/4 = x-6/3
aleksandrvk [35]
<h2><u>PROPORTIONAL EQUATION</u></h2><h3>Exercise</h3>

Apply the means-extremes property of proportions: this allows you to cross multiply:

                \boxed{\mathsf{\dfrac{x}{4} = \dfrac{x - 6}{3}}}

\mathsf{\dfrac{x}{4} \searrow \dfrac{x - 6}{3}}      ‏‏‎      ‏‏‎‎      \mathsf{\dfrac{x}{4} \nearrow \dfrac{x-6}{3}}‏‏‎‎

             \boxed{\mathsf{3x = 4(x - 6)}}

Apply the distributive property:

\mathsf{3x = 4(x-6)}

\mathsf{3x = 4(x) - 4(6)}

\mathsf{3x = 4x - 24}

Add 24 to both sides:

\mathsf{3x + 24 = 4x - 24 + 24}

\mathsf{3x + 24 = 4x}

Substract 3x to both sides

\mathsf{3x - 3x + 24 = 4x - 3x}

\mathsf{24 = 4x - 3x}

\large{\boxed{\mathsf{24 = x}}}

‎      ‏‏‎

<h3><u>Answer</u>. The value of x = 24.</h3>

‎      ‏‏‎

8 0
3 years ago
Simpifly 6/30 <br> ..... ........
ollegr [7]

Answer:

1/5

Step-by-step explanation:

Divide both numerator and denominator by 6:

1/5

7 0
3 years ago
Read 2 more answers
A circle has a diameter of 12 inches. What is its area in terms of π?
Natalka [10]

Answer:

36π

Step-by-step explanation:

Since you have to use terms of pi you just leave out pi out of the formula

A = πr² so it would be

A = r²       Radius is half of diameter so half of 12 = 6

A = 6²

A = 36

Than you add pi

36π

Hope this helped

4 0
3 years ago
Find the volume of this cylinder. Please help
algol13

Answer:

\boxed {\boxed {\sf 384 \ ft^3}}

Step-by-step explanation:

The volume is the space an object occupies. The volume formula for a cylinder is provided and it is:

V= \pi r^2 h

Where:

  • r= radius
  • h= height

The radius is the distance from the center of the circle to the edge, and it is 4 feet. The height is 8 feet. We are told to use 3 for pi.

  • r= 4 ft
  • h= 8 ft
  • π= 3

Substitute the values into the formula.

V= (3)(4 \ ft)^2 (8 \ ft)

Solve the exponent.

  • (4 ft)²= 4 ft * 4 ft = 16 ft²

V= (3)(16 \ ft^2)(8 \ ft)

Multiply the three numbers together.

V= 48 \ ft^2 (8 \ ft)

V= 384 \ ft^3

The volume of the cylinder is approximately <u>384 cubic feet.</u>

8 0
2 years ago
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