A town official claims that the average vehicle in their area sells for more than the 40th percentile of your data set. Using the data, you obtained in week 1, as well as the summary statistics you found for the original data set (excluding the super car outlier), run a hypothesis test to determine if the claim can be supported. Make sure you state all the important values, so your fellow classmates can use them to run a hypothesis test as well. Use the desсrіptive statistics you found during Week 2 NOT the new SD you found during Week 4. Because again, we are using the original 10 sample data set NOT a new smaller sample size. Use alpha ＝ .05 to test your claim. (Note: You will want to use the function ＝PERCENTILE.INC in Excel to find the 40th percentile of your data set. Hopefully this Excel function looks familiar to you from Week 2.) First determine if you are using a z or t-test and explain why. Then conduct a four-step hypothesis test including a sentence at the end justifying the support or lack of support for the claim and why you made that choice. I encourage you to review the Week 6 Hypothesis Testing PDF at the bottom of the discussion. This will give you a step by step example on how to calculate and run a hypothesis test using Excel. I DO NOT recommend doing this by hand. Let Excel do the heavy lifting for you. You can also use this PDF in Quizzes section. There were 5 additional PDFs that were created to help you with the Homework, Lessons and Tests in Quizzes section. While they won′t be used to answer the questions in the discussion, they are just as useful and beneficial. I encourage you to review these ASAP! These PDFs are also located at the bottom of the discussion. Once you have posted your initial discussion, you must reply to at least two other learner′s post. Each post must be a different topic. So, you will have your initial post from one topic, your first follow-up post from a different topic, and your second follow-up post from one of the other topics. Of course, you are more than welcome to respond to more than two learners.” Instructions: Make sure you include your data set in your initial post as well. You must also respond to at least 2 other students. Responses may include direct questions. In your first peer response post, look at the hypothesis test results of one of your classmates and explain what a type 1 error would mean in a practical sense. Looking at your classmate′s outcome, is a type 1 error likely or not? What specific values indicated this? In your second peer response post, using your classmate′s values, run another hypothesis test using this scenario: A town official claims that the average vehicle in their area Does Not sell for 80th percentile of your data set. Conduct a four-step hypothesis test including a sentence at the end justifying the support or lack of support for the claim and why you made that choice. Note: this test will be different than the initial post, starting with the hypothesis scenario. Use alpha ＝ .05 to test your claim.
Hypothesis Testing is a decision-making process called a Test of Significance.
There are 4 unique parts to Hypothesis Testing.
1) The Hypothesis Scenario. This includes the Null and Alternative scenarios.
a. Ho: Null Hypothesis
Ha or H1: Alternative Hypothesis
2) Z- Test Statistic
Z- Test Stat =
𝑝̂−𝑝0
𝑝 ∗𝑞
(√ 0 0)
𝑛
Where “𝑝0 ” is the hypothesized value and 𝑞0 = 1 − 𝑝0 .
3) P- value. The p-value tells you if something will be significant or not and if
you can Accept or Reject the claim. You will use the p-value to draw a
conclusion regarding the hypothesis test.
a. We will use =NORM.S.DIST function to find the p-value. It should
look familiar from Week 4.
4) Conclusion:
a. If the p-value is less than alpha (< α) then Reject Ho/Accept Ha.
b. If the p-value is greater than alpha (> α) then We Do Not Reject Ho.
c. The most common alpha value is .05. If no, alpha value is given it will
default to .05 but do note that alpha can also be, .10, .01, and .005 to
name a few. Essentially alpha can be any value the statistician
deems fit, but the most common values are .05, .01 and .10.
One last thing before we get to an example. There are 3 different scenarios that
are associated with the Hypothesis Scenario.
1) There is a Lower tailed (one tailed) Test or a Left Tailed Test. If the problem
asks if there a significant decrease or less than or lower than or fewer than,
then the problem is a lower tailed test. The “ 𝑝0
(Here we see that “𝑝0 ” is the hypothesized value and the
Greater Than Sign “>” lines up with the Ha)
3) There is a Two tailed Test. If the problem asks is there a significant
difference or statistical evidence or asks if it is not the same, then the
problem is a two-tailed test. The “≠” sign corresponds with the Ha. The
hypothesis scenario will look like:
a. Ho: 𝑝̂ = 𝑝0
Ha: 𝑝̂ ≠ 𝑝0
(Here we see that “𝑝0 ” is the hypothesized value and the
Greater Than Sign “≠” lines up with the Ha)
The hypothesized value is what we think should happen or what has been found
to be true in the past.
Now let’s continue to look at our car price data from Week 3. In Week 3, I asked
you to calculate the average and then find how many data points fell below the
average. We called this value p and then we found q. If we look back at my data
set, we see that p = .70 and q = .30.
We will call this 𝑝̂ = .70 and 𝑞
̂ = .30.
We want to run a test to see how close our data set is to a 50/50 spread? 50% of
the data would fall above the mean and 50% of the data would fall below the
mean, in a perfect world.
In other words, is there a difference between your data set and 50%? We will
calculate a 95% hypothesis to test this claim.
(Note: YES! I realize that some of you did see in your Week 3 forum that you did
get p = .50 and q = .50. If this is the case, your Test Statistic will be 0 and the pvalue will come out to be 1. That is fine, BUT it is still a good idea to go through
this example and make sure you can run a hypothesis test to get the correct
results. Extra practice never hurt anyone.)
Getting back to our test, this tells us that the hypothesized value is .50. The
hypothesis scenario will look like this:
1) Ho: 𝑝̂ = .50
Ha: 𝑝̂ ≠ .50
2) Z-Stat =
𝑝̂−𝑝0
̂ ∗𝑞
̂
𝑝
(√ )
𝑛
=
.70−.50
.50∗.50
(√
)
10
= 1.264911
Note: If your Z-Stat is negative that is fine. That does not mean the
problem is incorrect. And if your 𝑝̂ = .50, your Z-Stat would be 0 here
and that is fine also.
3) To find the p-value we will use the =NORM.S.DIST function. In Excel
type in =NORM.S.DIST(1.264911,TRUE) and hit Enter. We type in TRUE
because the hypothesis test is cumulative.
We see that the p-value = .897048. But remember this is in the Less Than form. If
we were running a Lower Tailed Test this would be our p-value. To find the pvalue for an Upper Tailed Test we would take p-value = 1 – .897048 = .102952.
Since we are running a Two Tailed Test, to get the correct p-value we would
multiply whichever p-value is smaller by 2. It will be different depending on the
test, so you need to make sure you use whichever one is smaller. Remember, pvalues CANNOT be greater than 1. If you get a p-value greater than 1, you did
something wrong.
p-value = .102952*2 = .205904. This is the p-value we will use for our conclusion.
If your Z-Stat is 0 then your p-value in this test will be 1. That is fine. Your p-value
can be 1 but it CANNOT be greater than 1.
4) Lastly, we need to state the conclusion. We will use alpha as .05. When
alpha is not stated it is defaulted to .05. .205904 > .05. The p-value is
greater than alpha. We DO NOT Reject Ho. Since we Do NOT Reject Ho,
this which means we CANNOT reject the claim that the distribution is
different from a 50/50 spread.
Vehicle type/ class
SUV
Sedan
Sedan
Sedan
SUV
Sedan
Sedan
SUV
Sedan
Sedan
Coupe
Year Make
Model
2022 Jeep
Grand Cherokee
2018 Nissan
Altima
2022 Acura
TLX
2021 Audi
A8
2021 BMW
X6
2022 Dodge
Charger
2022 Dodge
Challenger
2022 Dodge
Durango
2022 Mercedes E-Class
2022 Toyota
Camry
2022 Ferrari
812 GTS
Price
MPG (City) MPG (Highway)
45,555
19
26
12,763
26
37
39,611
21
29
74,946
17
26
62,600
21
26
34,798
19
30
32,106
19
30
39,298
19
26
52,804
23
31
28,950
28
39
407,450
12
15
