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frez [133]
3 years ago
14

Results of a survey conducted in 15 large cities within the U.S. finds that the average commute time one way to/from work is 25.

4 minutes. An executive of chamber of commerce believes that the commute time in her city is less than the amount reported by the survey. She randomly selects 25 commuters from her city and finds the average is 22.1 minutes and the standard deviation is 5.3 minutes. At ???? = 0.10, is her claim supported?
Mathematics
1 answer:
irina1246 [14]3 years ago
7 0

Answer:

We conclude that commute time in her city is less than the amount reported by the survey which is 25.4 minutes.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 25.4 minutes

Sample mean, \bar{x} = 22.1 minutes

Sample size, n = 15

Alpha, α = 0.10

Sample standard deviation, s = 5.3 minutes

First, we design the null and the alternate hypothesis

H_{0}: \mu = 25.4\text{ minutes}\\H_A: \mu < 25.4\text{ minutes}

We use one-tailed t(left) test to perform this hypothesis.

Formula:

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

Putting all the values, we have

t_{stat} = \displaystyle\frac{22.1 - 25.4}{\frac{5.3}{\sqrt{15}} } = -2.411

Now, t_{critical} \text{ at 0.10 level of significance, 14 degree of freedom } = -1.345

Since,                    

t_{stat} < t_{critical}

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Thus, there is enough evidence to conclude that commute time in her city is less than the amount reported by the survey which is 25.4 minutes.

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Step-by-step explanation:The area of a circle is pi times the radius squared (A = π r²)

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How many three-fourths are in 2
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3/4 times x=2
times both sides by 4/3 to clear fraction (4/3 times 3/4=12/12=1)
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there are 8/3 of them in 2

6 0
3 years ago
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A function is shown: f(x) = 36x² - 1.
givi [52]

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

<h3>What are equivalent functions?</h3>

Equivalent functions are different functions that have equal values when evaluated and compared

<h3>How to determin the equivalent function that best shows the x-intercepts on the graph?</h3>

The function is given as:

f(x) = 36x^2 - 1

Express 1 as 1^2

f(x) = 36x^2 - 1^2

Express 36x^2 as (6x)^2

f(x) = (6x)^2 - 1^2

Apply the difference of two squares.

This is represented as:

(a + b)(a - b) = a^2 - b^2

So, we have the following equation

f(x) = (6x - 1)(6x + 1)

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

Read more about equivalent function at:

brainly.com/question/2972832

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8 0
2 years ago
Alyssa accepted a new job at a company with a contract guaranteeing annual raises. Alyssa will get a raise of $4000 every year a
Ksivusya [100]

Answer:

S = 4000n + 4500

Step-by-step explained

S = 4500

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Answer - S=4000n + 45000

7 0
3 years ago
6. The perimeter of a parallelogram is 100 meters. The width of the parallelogram is 4 meters less than its length. Find the len
Ierofanga [76]

Answer:

x = 23, and y = 27.

Step-by-step explanation:

Lets say,

x = width

y = length

this means,

x(2) + y(2) = 100

It also says that the width is 4 meters less than the length.

if we put that into equation form it would look like this,

y - 4 = x

using these 2 equations, we can use the subustusion method to find the x.

x(2) + y(2) = 100

turns in to this :

step 1.     (y - 4) (2) + y(2) = 100 - given

step 2.      2y -8 + 2y = 100 -  distribute

step 3.      4y -8 = 100 - Combine like terms

step 4.       4y  = 108 - Get rid of the 8

step 5        4y/4  = 108 /4 - divide

step 6 .          y = 27

So if y is 27, then

x(2)  +  27(2) = 100

x(2) + 54 = 100

100 - 54 = 46, so x(2) is 46, but to get x, we need to divide 46 by 2, since x multiplied by 2 equals 46.

46  / 2 = 23 = x

so x = 23, and y = 27.

and the rule that y - 4 = x still applies, since 27 - 4 = 23.

I hope this wasn't confusing! It did take a long time tho.

5 0
3 years ago
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