I don’t know how to handle this Statistics question and need guidance.
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?
Peer 1: Lauren
Please refer to the Excel spreadsheet attached below for this forum post.
For this Hypothesis Test (AKA “Test of Significance”) we will be using a t-test. We are not using a z-test because z-tests relate to problems focused on proportions, which this problem is not. The 4-steps I will be taking to test the statement posed in the forum prompt are:
1. Stating the null hypothesis (H0) and alternative hypothesis (Ha or H1)
2. Finding the T-test state
3. Finding the P-value
4. Making a conclusion regarding the statement
First, I must determine what the 40th percentile of the data set is. To do this, I will use “=PERCENTILE.INC(E2:E11,0.4)”. This resulted in the value $29,280. The statement, “more than the 40th percentile” coincides with an upper-tailed (one-tailed) test in the form 29280f$ ” src=”https://edge.apus.edu/cgi-bin/latex.cgi?%5cinline%20%5Cbar%7Bx%7D%3E29280″>. This is the alternative hypothesis. The null hypothesis is thus .
Next, using the previously calculated mean ($31,930) and standard deviation ($6315.7739), I will calculate the T-Test State using . Let c=29280, n=10, =31930, and SD=6315.7739. Excel calculates the T-Stat to be 1.33.
Next, I will calculate the p-value using “=T.DIST.RT(J4,9)” where J4 is my T-State and 9 is the Degrees of Freedom (n-1). Excel calculated the p-value to be 0.108619.
Since alpha=0.05, the p-value=0.108619, and 0.05<0.108619, the p-value is greater than alpha. Thus, I do not reject H0. This means that I cannot reject the claim that the average sale price for a car in the town’s area is $29,280. However, I have proved the town official wrong because I could not accept Ha, which was their claim that the average vehicle sells for more than $29,280.
Peer 2: Martine
In this week’s scenario, a town official claims that the average vehicle in their area sells for more than the 40th percentile of your data set. Using my week 1 data, we’ll run a hypothesis test to determine if the claim can be supported.
Here are my important values:
40th Percentile: $39,183.40 (I found this by using =PERCENTILE.INC(E2:E11,0.4)
Therefore, the statement made by the town official is that their average vehicles sells for more than $39,183.40.
Our next step is to calculate the T-Test State using this formula: ̅− / (/√)
x̅ = 41,117
c = 39,183.40
SD = 16,398
n = 10
After plugging our data into the formula, we receive an answer of 0.37288572.
We then calculate the P-Value by using the following formula in Excel: =T.DIST.RT(J4,9), giving us a result of 0.358970.
Because my P-Value of 0.358970 is greater than the Alpha of .05, I cannot reject the claim made by the town official.