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Thepotemich [5.8K]
2 years ago
9

An automobile manufacturer has given its jeep a 56.1 miles/gallon (MPG) rating. An independent testing firm has been contracted

to test the actual MPG for this jeep since it is believed that the jeep performs under the manufacturer's MPG rating. After testing 200 jeeps, they found a mean MPG of 56.0. Assume the population standard deviation is known to be 2.1.
Is there sufficient evidence at the 0.02 level to support the testing firm's claim?
Mathematics
1 answer:
dsp732 years ago
7 0

Answer:

z=\frac{56-56.1}{\frac{2.1}{\sqrt{200}}}=-0.673    

Since we are conducting a left tailed test the p value would be:

p_v =P(Z  

Since we have that the p value is higher than the significance level of 0.02 we have enough evidence to conclude that the true mean is not significantly lower than 56.1 MPG the reference value.

Step-by-step explanation:

Information given

\bar X=56 represent the sample mean for the MPG

\sigma=2.1 represent the population standard deviation

n=200 sample size  

\mu_o =56.1 represent the reference value

\alpha=0.02 represent the significance level

t would represent the statistic

p_v represent the p value for the test

System of hypothesis

We want to check if the true mean is less than 56.1 MPG the reference value, the system of hypothesis would be:  

Null hypothesis:\mu \geq 56.1  

Alternative hypothesis:\mu < 56.1  

Since we know the population deviation the statistic is given by:

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

Replacing the info given we got:

z=\frac{56-56.1}{\frac{2.1}{\sqrt{200}}}=-0.673    

Since we are conducting a left tailed test the p value would be:

p_v =P(Z  

Since we have that the p value is higher than the significance level of 0.02 we have enough evidence to conclude that the true mean is not significantly lower than 56.1 MPG the reference value.

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If $-2 &lt; x \le 3,$ then find all possible values of $5x + 1.$ Give your answer in interval notation.
kotegsom [21]

Answer: (-9, 16]

This is the interval from -9 to 16. Exclude -9 but include 16.

=====================================================

Work Shown:

The idea is to multiply all sides by 5, then add 1 to all sides

-2 < x \le 3

5(-2) < 5x \le 5(3)

-10 < 5x \le 15

-10+1 < 5x+1 \le 15+1

-9 < 5x+1 \le 16

This converts to the interval notation  (-9, 16]

note: a curved parenthesis means "do not include this value in the solution set"; while a square bracket has us include the value. So we exclude -9 and include 16.

3 0
3 years ago
Train a travel 175 miles in a four hours. for train b y=43.5x represents its rate of speed over the same 4 hours which train tra
stepan [7]

Answer:

Train A is faster by a factor of 1.01

Step-by-step explanation:

Given:

Train A:

Distance = 175 Miles

Time = 4 Hours

Train B:

y=43.5x

To Find:

which train travels at a faster rate in by what factor  =?

Solution:

The speed of the train A = \frac{Distance}{time}

The speed of train A  =\frac{175}{4}

The speed of train A = 43.75 miles per hour

Speed of the train B is the slope of the given line

The standard equation of the slope of the line is

y = mx+b

where m is the slope

and we are given with

y = 43.5x

So comparing with the standard equation

m = 43.5

Hence the speed of train B is 43.5  miles per hours

Train A travels faster

Rate =\frac{\text{speed of train A}}{\text {Speed of train B}}

rate  = \frac{43.75}{43.5}

rate  =1.01

7 0
3 years ago
Can you please show me how to calculate the volume for each prism?
larisa [96]

Answer:

1st: volume = long x wide x high = 7 x [sqrt(25^2-7^2)] x 4 = 7 x 24 x 4 = 672

2nd: volume = area of base(circle) x high = pi x 9^2 x 8 = ~ 2035.8

3rd = volume = area of base(triangle) x high = [sqrt(3)/4] x 14^2 x 20 = ~1697.4

8 0
3 years ago
The exact value of cos5pi/12 is:​
jonny [76]

Step 1: Convert \frac{5\pi }{12}, which is in radians into degrees. To convert it multiply by \frac{180}{\pi }

\frac{5\pi }{12} =\frac{180}{\pi }

900/12

75

Step 2: 75 degrees isn't on the unit circle but 45 degrees and 30 degrees is. Since 45 + 30 = 75 you can use the cosine of 45 and 30 to find the exact value

cos45 = \frac{\sqrt{2} }{2}

cos30 =\frac{\sqrt{3} }{2}

Step 3: Add the cos45 and cos30 to get cos5pi/12

\frac{\sqrt{2} }{2} +\frac{\sqrt{3} }{2} = \frac{\sqrt{2}+\sqrt{3}}{2}

Hope this helped!

4 0
3 years ago
Calculate the stroke of a slider-crank where the crank radius is 4.13 inches and the coupler is 5 inches.
scoray [572]

Answer:

x=8.268 inches

Step-by-step explanation:

From the question we are told that:

Radius r=4.13

Coupler C= 5 inches.

Generally the equation for Stroke in a slider-crank Mechanism x is mathematically given by

 x=2* Radius

 x=2*4.13

 x=8.268 inches

5 0
3 years ago
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