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]
2 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]2 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
Sum1 helpppppppp meeeeeeeeeee
makkiz [27]

Answer:

16 in

Step-by-step explanation:

8x2

6 0
3 years ago
Which object has the mass of about one kilogram?
stira [4]

Answer:

A dictionary has the mass of about 1 killo so the book!

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Which ratio represents the tangent of an angle?
azamat

Answer:

option d.opposite / adjacent

Step-by-step explanation:

opposite /adjacent ratio represents the tangent of an angle .

hope it is helpful to you ☺️

3 0
2 years ago
Read 2 more answers
Trisha drew a pair of line segments starting from a vertex. Which of these statements best compares the pair of line segments wi
Ksju [112]

The <em>correct answer</em> is:


C) Line segments have two endpoints and a vertex is a common endpoint where two line segments meet.


Explanation:


A line segment is defined as a portion of a line that has two endpoints.


A vertex is defined as the common endpoint of two or more rays or line segments.


This makes C the correct option.

6 0
3 years ago
Read 2 more answers
More evaluation questions.....SIGH.
White raven [17]
Answer: 53

Steps:
Multiply to do 1/2x64+21
Reduce the numbers to get 32+21
Add to get 53!
4 0
3 years ago
Read 2 more answers
Other questions:
  • there are 28 students in a mathematics class. if 1/4 of the students are called to the guidance office,1/3 of the remaining stud
    7·2 answers
  • What value of x is in the solution set of 3(x-4) &gt; 5x + 2?
    10·1 answer
  • Sick-leave time used by employees of a firm in a course of one month has approximately normal distribution, with a mean of 200 h
    8·1 answer
  • Please help me with this algebra problem -3(x-5)+4x=24
    9·2 answers
  • Plzzzzzzzzz help <br> 20.41 rounded to the nearest hundredth
    6·2 answers
  • Write the rule for the transformation.
    13·1 answer
  • One morning, Muhammad's deli shop sells 15 sandwiches in 10 minutes. If the shop continues to sell sandwiches at the same rate,
    10·1 answer
  • What is the value of x?
    13·1 answer
  • HELP ASAP PLS ANSWER THE QUESTION IN THE PIC I GIV BRAINLEST AND LOTS OF POINTS TO CORRECT ANSWER
    8·1 answer
  • Simon is ordering a salad for lunch, he can choose one lettuce
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!