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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)

Attachment 1

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 <X<58,313) 0.0723008289 (=7%) ALPHA = α 0.5
$ 55,313.70 (mean minus 1500)
$ 58,313.70 (mean add 1500)
PROPORTIONAL CONFIDENCE INTERVAL
MEAN = 56,813.70 T CONFIDENCE INTERVAL Z- critical values
SD = 33061.48742 T= 2.2621571628 p-hat * q-hat= 1.9599639845
n = 10 SD/√n= 10454.9603060514 /n 0.24
P = 0.6 95% CONFIDENCE LEVEL= 23650.7633431052 SQRT (0.024) 0.024
Q = 0.4 UPPER CONFIDENCE LEVEL= $ 80,464.46 Z = 0.1549193338
LOWER CONFIDENCE LEVEL= $ 33,162.94 UPPER CONFIDENCE LEVEL= 0.3036363149
ALPHA = α (1-0.25=0.975) LOWER CONFIDENCE LEVEL= 0.9036363149 90%
degrees of freedom (DF) (10-1=9) 0.2963636851 30%

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

Attachment 2

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.