# Hypothesis testing I and II Responses

Open Posted By: ahmad8858 Date: 14/01/2021 High School Case Study Writing

INSTRUCTIONS: Provide (2) 150 words response for RESPONSES 1 AND 2 below. 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.

Attached are the instructions or word and excel docs for both responses to help with the post.

RESPONSE 1:

Step 1: Use T-test to verify the claim. (No standard deviation) You will need to use the descriptive data from week 2.

What is the Null and Alternative Hypothesis?

Ho: µ = 40th percentile

Ha: µ > 40th percentile

“A town official claims that the average vehicle in their area sells for more than the 40th percentile of your data set.”

• To find this calculation we will use the function      =PERCENTILE.INC ()
• =PERCENTILE.INC (E3:E12,0.4) I tried to just put the mean       down, but I didn’t get the same results.
• My 40th percentile is 46658

So now my Null and alternative hypothesis is:

Ho: µ = 46658

Ha: µ > 46658

Step 2: Calculate the test statistic: ???????? = ????̅− ????/ ???? √n

• From the data we have from excel
• ????= (Hypothesis Mean)
• ????̅ =56813.7 (Mean of sample)
• n= 10 (sample)
• s= 33061.487 (standard Deviation)

Step 3: Calculate the P-Value.

• To calculate the function for P-value you need =T. DIST.RT() but      this is considered a right tailed test.
• Next: Degrees of Freedom (DF)=n-1 (10-1=9)
• My P-Value = T. DIST.RT(0.9704,9) = 0.1786

According to the problem the problem given, the alpha α is 0.05, any my P-value is 0.1786.  This means that 0.1786>0.05 (P-value is more than alpha α).  So according to the data, we fail to reject the null hypothesis, because P-value is more than alpha α. There isn’t enough data to support the claim, that the average vehicle sells more than the 40th percentile.

(P.S. My new numbers are in Blue and Yellow.) PLEASE FEEDBACK IT WELCOME!!!!

RESPONSE 2:

For this week’s discussion I am conducting a t-test. I am conducting a t-test because the sample size is less than thirty and the variance is unknown. We were asked to test the hypothesis that the average vehicle in our vehicle spreadsheets would sell for more than the 40th percentile of our data set. For this test, alpha is 0.05. Here is my four-step hypothesis test:

Step 1: The Hypothesis Scenario

H₀: µ=c      or     H₀: µ=7690.2

Hₐ: µ>c      or     Hₐ: µ>7690.2

Based on the use of ‘>’ we know we are using a right tailed test.

Step 2: T-Test Statistic

???????? = (????̅− ????)/(????/√n)*

TS = (18588-7690.2)/6985.884873

TS = 1.560002805

*(????/√n) is the equation for Standard Error which can be found in excel using “=’Standard_Deviation’/SQRT(n) where n is the sample size of 10.

Step 3: P Value

Being a right tailed test, we used the Excel function ‘=T.DIST.RT(TS,n-1)”.

P Value =T.DIST.RT(1.560002805,10-1)

P Value = 0.076595373

Step 4: Conclusion

a) Our P Value is greater than alpha. p>α. 0.0766>0.05.

b) Due to our P Value being greater than alpha, we failed to reject the null hypothesis.

c) There is not enough evidence to support the claim that the average vehicle in the spreadsheet would sell for more than the 40th percentile.

-Andrew

Category: Mathematics & Physics Subjects: Calculus Deadline: 12 Hours Budget: \$100 - \$150 Pages: 2-3 Pages (Short Assignment)

## Sheet1

 Vehicles Type/Class Year Make Model Price MPG (City) MPG (Highway) Drive Type Qualitative Quantitative Qualitative Qualitative Quantitative Quantitative Quantitative Qualitative SUV 2021 Hyundai Genesis GV80 \$ 48,900.00 20 21 All Wheel Drive Hybrid/SUV 2021 Lexus GX \$ 58,665.00 16 20 All Wheel Drive Coupe 2017 Honda Accord EX \$ 16,791.00 27 36 2 Wheel Drive-Front Coupe 2014 Chevrolet Corvette \$ 38,990.00 15 23 2 Wheel Drive-rear Coupe 2020 Toyota Supra \$ 52,777.00 24 31 2 Wheel Drive-rear SUV 2021 Volkswagen Atlas \$ 43,320.00 16 22 2 Wheel Drive-Front Sedan 2020 BMW M340i \$ 50,998.00 22 30 All Wheel Drive Coupe 2020 Chevrolet Camaro LT \$ 27,996.00 19 29 2 Wheel Drive-rear Coupe 2020 BMW M8 \$ 119,994.00 15 21 All Wheel Drive Coupe 2020 Nissan GT-R \$ 109,706.00 16 22 All Wheel Drive Sports Car 2006 Maserati BirdCage 75th \$ 3,000,000.00 7 12 All Wheel Drive Before Adding Outlier DATA Mean: \$ 56,813.70 19 25.5 Median: \$ 49,949.00 17.5 22.5 STD: 33061.4874137736 4.18993503 5.5226805086 After Adding Outlier Data Mean: \$ 324,376.09 17.9090909091 24.2727272727 Median: \$ 50,998.00 16 22 STD: 887958.174169195 5.375026427 6.6346199453 56,813,70 Average under 6 p 0.6 q 0.4 P(x=4) 11.15% Exactly 4 P(x<5) = P (x ≤ 5-1) = P(x ≤ 4) 16.62% Fewer than 5 Hypothesis testing Hypothesis Testing P (x > 6)=1-p(x≤ 6)=1-p(x≤ 6) 38.23% More than 6 P(x≥4)=1-P(x≤ 4-1)=1-P(x≤ 3) 94.52% At least 4 Mean 56813.7 Ho: µ= 40th percentile 46668 <---=PERCENTILE.INC(E3:E12, 0.4) Standard Error 10454.9603060514 H1: µ ˃ 40th percentile Median 49949 Week 4 Mode ERROR:#N/A Ho: µ= 46668 New SD 16530.7437068868 Standard Deviation 33061.4874137736 H1: µ ˃ 46668 1 P(X< 56,313) mean minus \$500 0.4879351629 (= 48.79%) Sample Variance 1093061950.01111 Kurtosis 0.6212725883 Standard Error 10454.9603060514 <----(S/SQRT(n)) Skewness 1.1655058341 2 P(X>57,813) mean Add \$1000 0.4758982201 (=47.58%) Range 103203 Test Statics 0.9704197532 <---(Mean-40th Percentile)/SE Minimum 16791 Maximum 119994 Degree of Freedom 9 <---- N-1 3 P(X=56,813) 0.0000241334 (= 0%) Sum 568137 Count 10 P Value 0.1785963689 <----=T.DIS.RT(TEST STATICS, DF) Confidence Level(95.0%) 23650.7633431052 4 P(55,313

## Sheet2 (W_O Supercar)

 Column1 Mean 56813.7 Standard Error 10454.9603060514 Median 49949 Mode ERROR:#N/A Hypothesis Testing Standard Deviation 33061.4874137736 Sample Variance 1093061950.01111 Ho: µ= 40th percentile 56813.7 <---=PERCENTILE.INC(E3:E12, 0.4) Kurtosis 0.6212725883 H1: µ ˃ 40th percentile Skewness 1.1655058341 Range 103203 Ho: µ= 57593 Minimum 16791 H1: µ ˃ 57593 Maximum 119994 Sum 568137 Standard Error 0 <----(S/SQRT(n)) Count 10 Confidence Level(95.0%) 23650.7633431052

## Sheet 3 (With SuperCar)

 With Supercar Mean 351923.7 Standard Error 294415.077482457 Median 51887.5 Mode ERROR:#N/A Standard Deviation 931022.222339516 Sample Variance 866802378490.011 Kurtosis 9.965500215 Skewness 3.1549042033 Range 2983209 Minimum 16791 Maximum 3000000 Sum 3519237 Count 10 Confidence Level(95.0%) 666013.176362728

## Sheet1

 VEHICLE CLASS YEAR MAKE MODEL TRADE IN VALUE MPG (city) MPG (hw) COMBINED Tank Size (Gal.) Fuel Economy* Pickup 2017 Ford F-150 XLT \$25,562 18 23 20 23 460 Sedan 2013 Dodge Dart Rallye \$7,428 25 36 29 15.8 458.2 Pickup 2015 GMC Sierra 1500 SLE \$11,390 14 19 16 26 416 Sedan 2012 Ford Fusion SE \$7,865 23 33 26 17.5 455 Station Wagon 2012 VW Jetta SportWagon TDI \$9,108 29 37 32 14.5 464 Hatchback 2017 Mitsubishi Mirage ES \$7,328 33 41 36 9.2 331 Sedan 2010 Kia Optima LX \$5,445 22 32 25 16.4 410 Coupe 2018 Dodge Challenger R/T \$27,678 16 25 19 18.5 351.5 Pickup 2004 GMC Sonoma SLS \$6,823 14 18 16 17 272 SUV 2019 Tesla Model X Long Range \$77,255 99e 93e 96e N/A 371** Qualitative Quantitative Qualitative Qualitative Quantatative Quantatative Quantatative Quantatative Quantatative Quantatative *Fuel Economy = Tank Size x Combined MPG **The Tesla Model X Long Range SUV is a fully electric car and does not use gasoline Mean (x): \$18,588 Step 1: H0: µ=c H0: µ=7690.2 Median: \$8,487 Ha: µ>c Ha: µ>7690.2 Standard Deviation: 22091.3076711684 Alpha: 0.05 Sample Size (n): 10 Standard Error: 6985.8848732442 p (success) 0.70 Step 2: T-test Statistic: 1.5600028053 q (failure) 0.30 Step 3: p-value: 0.0765953732 40th Percentile (c): 7690.2 Step 4a: p>α 0.0766>0.05 Step 4b: Failed to reject null hypothesis. Step 4c: There is not enough evidence to support the alternative hypothesis.