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

kow [346]

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.

8 0

2 years ago

How did you compute sums of dollar amounts that were not whole numbers?

soldier1979 [14.2K]

Answer:

$7.34

Step-by-step explanation:

To compute sum of dollars that are not whole numbers. Using the sum of$5.89 and$1.45 as an illustration :

$5.89 + $1.45

Taking the whole numbers first:

$5 + $1 = $6

Take the sum of the decimals :

$0.89 + $0.45 = $1.34

Sum initial whole + whole of sum of decimal

$6 + $1 = $7

Remaining decimal : $1.34 - $1 = $0.34

$7 + $0.34 = $7.34

8 0

3 years ago

What is the meaning of opposites

skelet666 [1.2K]

a person or thing that is totally different from or the reverse of someone or something else.

4 0

3 years ago

A wave on a rope has a wavelength of 2.0 m and a frequency of 2.0 Hz. What is the speed of the wave?

Vsevolod [243]

depends on the tension and the length of the rope

4 0

3 years ago

Can you guys and gals help me

professor190 [17]

Answer:

1. B 2. B 3. D 4. A 5. A 6. A 7. B 8. C

Step-by-step explanation:

1. 6 and 8 are right next to each other. Making them 'adjacent angles' as 'adjacent' means 'next to'

2. 2 and 3 are vertically opposite angles, and these angles are equal to each other

3. 3 and 6 are alternate angles. These angles form a 'Z' shape

4. Similar to q2, 1 and 4 are vertically opposite angles

5. Yes they are similar because there are two angles which equal

6. The angles of the big triangle will correlate to the small triangle, therefore x is 40

7. Similar triangles will have the same angles. The top angle of the small triangle is 60, as stated in the big triangle, and 70 is given. The sum of interior angles of a triangle is 180. So, add 60 and 70, then minus from 180

8. Again, same concept as q7, the angles are given to you and you just need to correspond each angle to its respective area, then minus the total of the two given angles from 180

Hope this helped you!!

7 0

3 years ago