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tangare [24]
3 years ago
15

It is claimed that automobiles are driven on average more than 20,000 kilometers per year. To test this claim, 100 randomly sele

cted automobile owners are asked to keep a record of the kilometers they travel. Would you agree with this claim if the random sample showed an average of 23,500 kilometers and a standard deviation of 3900 kilometers? Use a P-value in your conclusion.
Mathematics
1 answer:
kow [346]3 years ago
8 0

Answer:

t=\frac{23500-20000}{\frac{3900}{\sqrt{100}}}=8.974      

p_v =P(t_{99}>8.974)=9.43x10^{-15}  

If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we to reject the null hypothesis, and the actual mean is significantly higher than 20000.      

Step-by-step explanation:

1) Data given and notation      

\bar X=23500 represent the sample mean  

s=3900 represent the sample standard deviation      

n=100 sample size      

\mu_o =2000 represent the value that we want to test    

\alpha represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)      

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the true mean is higher than 20000, the system of hypothesis would be:      

Null hypothesis:\mu \leq 2000      

Alternative hypothesis:\mu > 2000      

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:      

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)      

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic      

We can replace in formula (1) the info given like this:      

t=\frac{23500-20000}{\frac{3900}{\sqrt{100}}}=8.974      

Calculate the P-value      

First we need to calculate the degrees of freedom given by:  

df=n-1=100-1=99  

Since is a one-side upper test the p value would be:      

p_v =P(t_{99}>8.974)=9.43x10^{-15}  

Conclusion      

If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we to reject the null hypothesis, and the actual mean is significantly higher than 20000.      

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5. Brianna earns $19,500 per year. Lisa earns $1,000 per month. Write a numerical expression that represents how much more Brian
Morgarella [4.7K]

Answer:

19,500 - (1,000 x 12) = X

Brianna earns $ 7,500 more than Lisa per year.

Step-by-step explanation:

Given that Brianna earns $ 19,500 per year and Lisa earns $ 1,000 per month, to write a numerical expression that represents how much more Brianna earns per year than Lisa the following calculations and equations must be performed:

19,500 - (1,000 x 12) = X

19,500 - 12,000 = X

7,500 = X

Thus, Brianna earns $ 7,500 more than Lisa throughout the year.

6 0
3 years ago
A salesman sells a car for $37,000 and earns 8.5% commission. How much commission does he earn?
nevsk [136]

Answer:

4,352 dollars

Step-by-step explanation:

6 0
2 years ago
It’s for question number 2 and please help I would really appreciate that
motikmotik

Answer:

Step-by-step explanation:

Ok so first, you need to do 2.5 - 1.125.

Make 2.5--->2.500

Subtract: 2.500

                1.125

             =1.375 liters

           

3 0
3 years ago
The symbol ∪ represents the union of events. The union of two events A and B results in an event that contains all the sample po
Degger [83]

Answer:

AUB = {E1, E2, E4, E6, E7}

Step-by-step explanation:

Since we are to look for the union of the two sets, therefore we combine all the sample points that are contained in A and B without repeating any sample even if such sample occur in both sets. For example, E4 occurs in event A and B and as such will only be repeated once in the union of the two events.

AUB = {E1, E2, E4, E6, E7}

Note that the way you arrange does not matter as well.

I hope you find this solution useful?

8 0
3 years ago
Solve the equation for x.
Degger [83]

Answer:

x=-\frac{11}{8}

Step-by-step explanation:

Hi there!

(x - 4) - (x + 7) = 8x

Open up the parentheses

x - 4 - x - 7 = 8x

Combine like terms

x -x - 4 - 7 = 8x\\-4-7=8x\\-11=8x

Divide both sides by 8 to isolate x

-\frac{11}{8}=x

I hope this helps!

4 0
3 years ago
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