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
Agata [3.3K]
3 years ago
12

Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the pre

vious 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis?
Mathematics
1 answer:
choli [55]3 years ago
4 0

Answer:

z=\frac{0.4 -0.48}{\sqrt{\frac{0.48(1-0.48)}{115}}}=-1.717  

p_v =P(z  

So the p value obtained was a very low value and using the significance level given \alpha=0.1 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that have traded in their old car is lower than 0.48 or 48%.  

Step-by-step explanation:

Data given and notation

n=115 represent the random sample taken

X=46 represent the number of people that have traded in their old car.

\hat p=\frac{46}{115}=0.4 estimated proportion of people that have traded in their old car

p_o=0.48 is the value that we want to test

\alpha=0.1 represent the significance level

Confidence=90% or 0.9

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion is less than 0.48.:  

Null hypothesis:p\geq 0.48  

Alternative hypothesis:p < 0.48  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.4 -0.48}{\sqrt{\frac{0.48(1-0.48)}{115}}}=-1.717  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.1. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(z  

So the p value obtained was a very low value and using the significance level given \alpha=0.1 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that have traded in their old car is lower than 0.48 or 48%.  

You might be interested in
And the other answer???
il63 [147K]

Answer:

What other answer?

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Max lost 23 pounds while on a diet. He
san4es73 [151]
184+23=w
207=w
That’s the answer 207
3 0
3 years ago
What is the area of a square if one side is 25 feet long?
QveST [7]
The area of the square is 100ft
5 0
3 years ago
Read 2 more answers
I already solved this problem. I just need help with the HINT part.
frutty [35]
x+y=25 \\ y=25-x~~Other~number~in~terms~of~x \\ \\ x^2+y^2=313 \\ x^2+2xy+y^2=313+2xy \\ (x+y)^2=313+2x(25-x) \\ \frac{25^2-313}{2} =25x-x^2 \\ x^2-25x+156 \\ \\ \Delta =(-25)^2-4\times 1\times 156 \\ \Delta =625-624 \\ \sqrt{\Delta}=1 \\ \\ x= \frac{25 \pm 1}{2} \\ x= \left \{ {{x_1=13} \atop {x_2=12}} \right.

     The number "x" is given by:
y= \left \{ {{y_1=25-13 \rightarrow~y_1=12} \atop {y_1=25-12 \rightarrow ~y_1=13}} \right.
  
     Therefore, we have:

\boxed {S=({12,13})} \rightarrow~The~curly~braces~does~not~want~appear~here.
8 0
3 years ago
3 = x/12 - 4 what is x
alexgriva [62]

Answer:

x=84

Step-by-step explanation:

Add 4 on both sides

3=x/12-4

7=x/12

Multiply both sides by 12

(12)7=x/12(12)

84=x

Hope this helps! :)

3 0
3 years ago
Read 2 more answers
Other questions:
  • Match the polynomial in the left column with its descriptive feature in the right
    14·1 answer
  • What is the value of n?
    5·1 answer
  • A local restaurant advertises that the mode cost of their most popular meals is $8. If the costs of their most popular meals are
    6·2 answers
  • Correct answer will get brainliest
    14·1 answer
  • Please help its math
    7·2 answers
  • Which of the following expressions represents the addition of 7² and 7³?
    15·2 answers
  • Jayson used 0.5 cup of kernels to make 16 cups of popcorn. How many cups of popcorn would he make if he used 0.75 cup of kernels
    6·2 answers
  • SOLVE THIS QUESTION WITH FULL STEPS...THANKS
    5·1 answer
  • Help help help help please
    5·1 answer
  • Is 3.22×104 equal to 32,200?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!