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Brilliant_brown [7]
3 years ago
10

A random sample of 100 observations from a quantitative population produced a sample mean of 22.8 and a sample standard deviatio

n of 8.3.
Use the p-value approach to determine whether the population mean is different from 24.

Explain your conclusions. (Use α = 0.05.)

State the null and alternative hypotheses. H0: μ = 24 versus Ha: μ ≠ 24 H0: μ = 24 versus Ha: μ > 24 H0: μ ≠ 24 versus Ha: μ = 24 H0: μ = 24 versus Ha: μ < 24 H0: μ < 24 versus Ha: μ > 24

Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) z = p-value = State your conclusion.
Mathematics
1 answer:
natima [27]3 years ago
7 0

Answer:

We conclude that the population mean is 24.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 24

Sample mean, \bar{x} = 22.8

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 8.3

First, we design the null and the alternate hypothesis

H_{0}: \mu = 24\\H_A: \mu \neq 24

We use Two-tailed z test to perform this hypothesis.

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{22.8 - 24}{\frac{8.3}{\sqrt{100}} } = -1.44

We calculate the p-value with the help of standard z table.

P-value = 0.1498

Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.

Now, z_{critical} \text{ at 0.05 level of significance } = \pm 1.96

Since,  the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.

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Answer:

x = 9

Step-by-step explanation:

You can solve this problem by isolating the variable.

3-√x = 0  

√x = 3 (add √x to both sides of the equation)

x = 9 (square both sides of the equation)

8 0
3 years ago
Weather
Crank

Answer:

It snowed for 6 days in November

Step-by-step explanation:

Since there are 30 days in November

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5 0
2 years ago
This question is from the similarity chapter. It would be really kind of you if you would answer this question.
katen-ka-za [31]

Answer:

a) 1650 m

b) 1677.05 m

Step-by-step explanation:

Hi there!

<u>1) Determine what is required for the answers</u>

For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.

For part B, we're asked to solve for the length of the road, or the length of AB.

<u>2) Prove similarity</u>

In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).

How do we know they're similar?

  1. Angles AYX and ACB are corresponding and they both measure 90 degrees
  2. Both triangles share angle A

Therefore, the two triangles are similar because of AA~ (angle-angle similarity).

<u>3) Solve for part A</u>

Recall that we need to find the length of AC.

First, set up a proportion. XY corresponds to BC and AY corresponds to AC:

\frac{XY}{BC}=\frac{AY}{AC}

Plug in known values

\frac{2}{300}=\frac{11}{AC}

Cross-multiply

2AC=11*300\\2AC=3300\\AC=1650

Therefore, the road will rise 300 m over a horizontal distance of 1650 m.

<u>4) Solve for part B</u>

To find the length of AB, we can use the Pythagorean theorem:

a^2+b^2=c^2 where c is the hypotenuse of a right triangle and a and b are the other sides

Plug in 300 and 1650 as the legs (we are solving for the longest side)

300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c

Therefore, the length of the road is approximately 1677.05 m.

I hope this helps!

3 0
3 years ago
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Answer

Step-by-step explanation:

If you deposit money, your bank account shows it as +3

3 degrees below zero = - 3 o F which is darn cold.

3 floors below ground level = - 3 floors below ground level

3 feet above sea level = +3 feet

3 degrees about 0 = + 3

3 dollars lost = -3 dollars.

5 0
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a foreman must order enough sod to cover a dirt area 36 feet wide by 28 feet long. each piece of sod is 3 feet long and 12 inche
Andrews [41]

If we divide the area we have to cover by the area of a piece, we will get the number of pieces needed:

n=\dfrac{\text{dirt area}}{\text{piece area}}=\dfrac{36\times 28}{3\times 12} = \dfrac{36\times 28}{36}=28

3 0
2 years ago
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