ASSIGNMENT: 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 descriptive 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. MY ANSWER: Data Set: $37,150.00 $76,095.00 $22,045.00 $35,000.00 $39,900.00 $37,305.00 $86,995.00 $27,655.00 $79,990.00 $32,000.00 Descriptive Statistics: Price Mean 47413.5 Standard Error 7557.303974 Median 37227.5 Mode #N/A Standard Deviation 23898.29353 Sample Variance 571128433.6 Kurtosis -1.041298135 Skewness 0.895717776 Range 64950 Minimum 22045 Maximum 86995 Sum 474135 Count 10 Confidence Level(95.0%) 17095.80932 40th Percentile: 36290.00 Type of test: t-test, due to our dataset being less than 30. Hypothesis: Ho: mean = $36,290.00 Ha: mean > $36,290.00 Level of Significance: 0.05 Critical Value: 2.262157163 "=T.INV(0.975,9)" Test Statistic: 1.471887334 p-value: 0.087567468 "=T.DIST.RT(1.471887334,9)" Results: 0.087567468 > 0.05 Since p is greater than the significance level (alpha), we fail to reject Ho. We can conclude the town official's claim that the average vehicle in their area sells for more than the 40th percentile of your data set is false. My teacher response: since the alternative hypothesis is Ha: µ > 36290 which is a right-tailed test, you should not use T.INV.2T to find the critical value. This command is used for a two-tailed test. This of course affects the p-value and potentially your conclusions.
Can someone please help me to better understand?
ASSIGNMENT:
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
(Note: You will want to use the
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.
MY ANSWER:
Data Set:
| $37,150.00 |
| $76,095.00 |
| $22,045.00 |
| $35,000.00 |
| $39,900.00 |
| $37,305.00 |
| $86,995.00 |
| $27,655.00 |
| $79,990.00 |
| $32,000.00 |
Descriptive Statistics:
| Price | |
| Mean | 47413.5 |
| Standard Error | 7557.303974 |
| 37227.5 | |
| #N/A | |
| Standard Deviation | 23898.29353 |
| Sample Variance | 571128433.6 |
| Kurtosis | -1.041298135 |
| Skewness | 0.895717776 |
| 64950 | |
| Minimum | 22045 |
| Maximum | 86995 |
| Sum | 474135 |
| Count | 10 |
| Confidence Level(95.0%) | 17095.80932 |
40th Percentile:
36290.00
Type of test:
t-test, due to our dataset being less than 30.
Hypothesis:
Ho: mean = $36,290.00
Ha: mean > $36,290.00
Level of Significance:
0.05
Critical Value:
2.262157163 "=T.INV(0.975,9)"
Test Statistic:
1.471887334
p-value:
0.087567468 "=T.DIST.RT(1.471887334,9)"
Results:
0.087567468 > 0.05
Since p is greater than the significance level (alpha), we fail to reject Ho.
We can conclude the town official's claim that the average vehicle in their area sells for more than the 40th percentile of your data set is false.
My teacher response:
since the alternative hypothesis is
Ha: µ > 36290
which is a right-tailed test, you should not use T.INV.2T to find the critical value. This command is used for a two-tailed test.
This of course affects the p-value and potentially your conclusions.
I don't understand how my calculating the critical value incorrectly could affect my p-value and my conclusion. Can someone explain how this could cause issues?
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