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
lapo4ka [179]
3 years ago
7

To Test the ability of auto mechanics to identify simple engine problems, an automobile with a single suchproblem was taken to 7

2 different car repair facilities. Only 42 out of 72 mechanics who worked on the carcorrectly identified the problem. Does this strongly indicate that the true proportion of mechanics who couldidentify this probelm is less than.75? Compute the p-value and reach a conclusion.
Mathematics
1 answer:
dedylja [7]3 years ago
7 0

Answer:

z=\frac{0.583 -0.75}{\sqrt{\frac{0.75(1-0.75)}{72}}}=-3.273  

p_v =P(Z  

So the p value obtained was a very low value and using any significance level for example \alpha=0.05 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 mechanics who worked on the carcorrectly identified the problem is significantly less than 0.75.  

Step-by-step explanation:

1) Data given and notation  

n=72 represent the random sample taken

X=42 represent the mechanics who worked on the carcorrectly identified the problem

\hat p=\frac{42}{72}=0.583 estimated proportion of mechanics who worked on the carcorrectly identified the problem

p_o=0.75 is the value that we want to test

\alpha represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.75:  

Null hypothesis:p\geq 0.75  

Alternative hypothesis:p < 0.75  

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.

3) Calculate the statistic  

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

z=\frac{0.583 -0.75}{\sqrt{\frac{0.75(1-0.75)}{72}}}=-3.273  

4) 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 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 any significance level for example \alpha=0.05 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 mechanics who worked on the carcorrectly identified the problem is significantly less than 0.75.  

You might be interested in
Mr gomez gave his class a test on 20 spelling words. Only one of the following percents is possible as a percent of the 20 words
yawa3891 [41]
The answer would be a I believe so
5 0
3 years ago
Read 2 more answers
Find the mean of the numbers<br> 1, -3, -10<br> -15, 4, -22<br> -7.5, 3, -6.5
Travka [436]

Answer:

13. -4 14. -11 15. -\frac{11}{3}

Step-by-step explanation:

13. (1-3-10)/3

14. (-15+4-22)/3

15. (-7.5+3-6.5)/3

5 0
3 years ago
Read 2 more answers
Sweet T is making a double batch of cupcakes. He puts them in the oven at 6:50 that needs to bake for 25 minutes. When should sw
Serhud [2]
He should take out the cupcakes at 7:15! Hope this helps :D
8 0
3 years ago
7g – 2g + g + 3g = 18
In-s [12.5K]
G = 2

Hope This Is Sufficient !!
5 0
3 years ago
Read 2 more answers
If p=1/3 what is 12p
anyanavicka [17]

Step-by-step explanation:

Given

p \:  =  \frac{1}{3}  \\ 12p \:  = 12 \times  \frac{1}{3}  \\  = 4

Hope it will help :)

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which two equations would be most appropriately solved by using the quadratic formula?
    13·2 answers
  • How do you graph: y = 4√x
    8·2 answers
  • Which decimal is equivalent to 5/20
    8·1 answer
  • 6<br> Factor the expression.<br> 4z- 28
    11·1 answer
  • I need to solve for x
    9·1 answer
  • Jazz emerged as musicians combined elements of
    13·2 answers
  • Factor 6x^9 - 15x^5
    6·1 answer
  • During hockey season, Pete scored goals on 15% of the shots he took. If he scored 75 goals, how many shots did he take?
    13·1 answer
  • A little boy stands on a carousel and rotates around the road four times. The distance between the little boy and the center of
    11·1 answer
  • Mrs. Hernandez earns $35.60 per hour and in one week earned $854.40. For how many hours did she work last week? What expression
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!