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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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A scientist mixes water (containing no salt) with a solution that contains 35% salt. She wants to obtain 245 ounces of a mixture
sesenic [268]

Answer:

140 ounces of water and 105 ounces of 35% salt solution.

Explanation:

Let x be the ounces of water that need to be added and y be the ounces of 35% solution that need to to be added.

We know that the total of ounces of water and of 35% solution must be 245 ounces:

x+y=245

35% of  x is the salt, and since no salt is added with addition of y  liters of water, this must be equal to the amount of salt in the final 15% solution:

0.35x=0.15*245

we solve for  x and get:

x=105

We put this value into x+y=245 and solve for y to get:

y=140

Thus we have 140 ounces of water and 105 ounces of 35% solution.

8 0
3 years ago
The half of the circle equals 764747575674 cm. <br> What's the whole circle?
Greeley [361]
Times by 2
1.529495e9 cm
3 0
3 years ago
Can someone help me
Morgarella [4.7K]
The total cost would be $4,050. Hope this helps!
7 0
2 years ago
Read 2 more answers
Solve the following system using the substitution, elimination, or graphing method for the x coordinate:
igomit [66]
Hey there!

To solve this system of equations, you will need to get one of the terms in both equations to cancel out to zero. If there isn't a term that you can cancel out, you can multiply either or both equations to make that term. There's no wrong way to do this, just as long as you make sure that you double check whether your should add or subtract. This is easier shown than explained, so refer below:

<span>  x + y = +1
5x + y = –6

</span>–1(x + y = +1)
   5x + y = –6

–x – y = –1
5x + y = –6

You can see that once we combine these equations by adding, the y term will become 0, eliminating it. This is necessary for solving the system, so make sure you do it. Also, remember to distribute the term that you need to to all of the numbers in the equation! After that, just solve for the variable that's still in the equation. 

   –x – y = –1
+ 5x + y = –6

4x + 0y = –7
4x = –7
x = –1.75

Now, just plug the value we found for x into either one of your equations in the original system as it's presented in your problem. 

x + y = 1
–1.75 + y = 1
+1.75        +1.75

y = 2.75

All that's left to do is check your point (–1.75, 2.75). If it's true for both equations, your answer is correct!

–1.75 + 2.75 = 1
<span>5(–1.75) + 2.75 = –6

</span>(–1.75, 2.75) is the solution to your system. 

Hope this helped you out! :-)
3 0
3 years ago
Let the correct answer
grigory [225]

Answer:

c i think sorry if i get it wrong

Step-by-step explanation:

6 0
2 years ago
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