Question

Vehicle Name	SuggestedRetailPrice
BMW 325Ci 2dr	30795
BMW 325Ci convertible 2dr	37995
BMW 325i 4dr	28495
BMW 325xi 4dr	30245
BMW 330Ci 2dr	36995
BMW 330Ci convertible 2dr	44295
BMW 330i 4dr	35495
BMW 330xi 4dr	37245
BMW 525i 4dr	39995
BMW 530i 4dr	44995
BMW 545iA 4dr	54995
BMW 745i 4dr	69195
BMW 745Li 4dr	73195
Mercedes-Benz C230 Sport 2dr	26060
Mercedes-Benz C240 4dr	32280
Mercedes-Benz C240 4dr	33480
Mercedes-Benz C32 AMG 4dr	52120
Mercedes-Benz C320 4dr	37630
Mercedes-Benz C320 Sport 2dr	28370
Mercedes-Benz C320 Sport 4dr	35920
Mercedes-Benz CL500 2dr	94820
Mercedes-Benz CL600 2dr	128420
Mercedes-Benz CLK320 coupe 2dr (convertible)	45707
Mercedes-Benz CLK500 coupe 2dr (convertible)	52800
Mercedes-Benz E320 4dr	48170
Mercedes-Benz E500 4dr	57270
Mercedes-Benz S430 4dr	74320
Mercedes-Benz S500 4dr	86970

In what follows use any of the following tests/procedures: Regression, multiple regressions, confidence intervals, one-sided t-test or two-sided t-test. All the procedures should be done with 5% P-value or 95% confidence interval

Upload CARS data. SETUP: It is believed that Mercedes’ prices (Suggested price) are different than BMW’s. Given the data your job is to confirm or disprove this belief. (CAREFULL: sort the data in order to extract the needed information).

1. What test/procedure did you perform?

• a. One-sided t-test
• b. Two-sided t-test
• c. Regression
• d. ​​Confidence interval

2. What is the P-value/margin of error?

• a. 0.161902527
• b. 0.080951264
• c. 6.149555
• d. 8.065421
• e. ​​None of these

3. Statistical interpretation

• a. Since P-value is very small we are confident that the average Price is above 40000.
• b. Since P-value is large we cannot claim that the averages are different.
• c. Since P-value is very small we are confident that the slope of regression line is not zero.
• d. ​​None of these.

4. Conclusion

• a. Yes, I am confident that the above assertion is correct.
• b. No, we cannot claim that the above assertion is correct.

Answer 1

1. Since Mercedes and BMW are two different brands and prices are collected for these brands, the appropriate test is two sample t test, of course, assuming normality.

Since, we are interested in testing whether Mercedes’ prices (Suggested price) are different than BMW’s or not, the hypothesis is two sided. Then correct option is Two-sided t test. (option b)

2. The boxplot of prices show that the variability of Mercedes is quite higher than that of BMW. Hence, we performed a tw-sided t test assuming different variances and get the p value as .1630

However, if we forcefully assume equal variances, we get the corresponding p value as 0.178.

Thus option e is correct.

3. option b: Since P-value is large we cannot claim that the averages are different.

4. Option b. No. we cannot claim that the above assertion is correct.