1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.      

You might be interested in
If b < 0 and a/b > c/b, then what is the relationship between a and c?
serg [7]

Answer:

  • a < c

Step-by-step explanation:

<u>Given inequality:</u>

  • a/b > c/b

<u>Since b is negative, when multiplied by b, the inequality changes to opposite direction:</u>

  • b(a/b) < b(c/b)
  • a < c

3 0
3 years ago
Kelsey had 8 entries in her science journal. Last week, she wrote x more entries. How many entries are in her science journal no
In-s [12.5K]

Answer:

Kelsey has 8 plus more entries

8 + x

5 0
2 years ago
What is the answer to this?
Leya [2.2K]

\huge\bold\purple{2/3:}

6 0
3 years ago
Amber has 36 smarties to share among herself and 3 friends. How many smarties will each of them Receive?
ki77a [65]
There are 4 people in total
(including herself)
so 36 smarties should be evenly distributed among 4 people

so answer = 36/4 = 9
7 0
2 years ago
Product of 3.24<br><br> 0.45 x 0.72 <br><br> 0.45 x 72<br><br> 4.5 x 0.7<br><br> 4.5 x 7.2
natta225 [31]

Answer:

4.5 x 0.72

Step-by-step explanation:

I AM ASSUMING THAT YOU FORGOT TO ADD 2 AFTER 0.7 IN 4.5 x 0.7

4 0
2 years ago
Read 2 more answers
Other questions:
  • I need help. i dont get it
    10·2 answers
  • 2 is subtracted from a number, and then the the difference is multiplied by 5. The result is 30
    8·2 answers
  • I need help on this problem i don’t understand what to do
    6·1 answer
  • Write an equation to model the following situation.
    14·2 answers
  • The hypotenuse of a 45°-45°-90° triangle measures units.What is the length of one leg of the triangle?
    8·1 answer
  • Lloyd has a fish tank that is 8 inches high, 14 inches long, and 6 inches wide. A fish tank has a length of 14 inches, height of
    6·1 answer
  • Evaluate the expression for x = - 5 and y = 7 <br><br> 2x+3y-11
    5·1 answer
  • Solve for x in the figure below
    11·2 answers
  • I have $28.65 worth of coins. The coins are in denominations of 1, 5, 10, 25, 50 cents and $1.
    6·2 answers
  • Heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!