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Two manufacturers of sport utility vehicles claim that the sharpness of the turning radius for their SUV is better than all other SUVs on the market. John randomly selected 30 professional sports car drivers to test the manufacturers' claims. The drivers were all experienced in driving both manufacturers' SUVs as well as competing SUVs on the market. He asked 15 drivers their opinion of vehicle A and 15 drivers their opinion of vehicle B. The drivers' opinions on both SUV manufacturers' claims are shown in the table.

\begin{tabular}{|c|c|c|}
\hline
& Vehicle A & Vehicle B \\
\hline
Agreed & 11 & 13 \\
\hline
Disagreed & 4 & 2 \\
\hline
\end{tabular}

Given John's data collection method and findings, what conclusion can be made?

A. Both SUV manufacturers' claims are true, but the turning radius of vehicle [tex]$B$[/tex] is sharper than the turning radius of vehicle [tex]$A$[/tex].
B. Neither of the claims are correct.
C. Only the claim for vehicle B is true because more people agree with their claim.
D. Only the claim for vehicle A is true because 11 out of 15 people agree with their claim.



Answer :

GinnyAnswer
To address John's inquiry about the SUV manufacturers' claims regarding the turning radius of their SUVs, let's analyze the data he collected and determine what conclusion can be drawn.

Given the data:

- For Vehicle A:
- 15 drivers tested the vehicle.
- 11 drivers agreed with the manufacturer's claim.
- 4 drivers disagreed with the manufacturer's claim.

- For Vehicle B:
- 15 drivers tested the vehicle.
- 13 drivers agreed with the manufacturer's claim.
- 2 drivers disagreed with the manufacturer's claim.

Let's consider each option in turn:

A. "Both SUV manufacturers' claims are true, but the turning radius of vehicle B is sharper than the turning radius of vehicle A."

This option suggests that the manufacturers' claims for both vehicles are correct. Both vehicles received positive feedback (11 out of 15 for Vehicle A, and 13 out of 15 for Vehicle B). However, it also implies that Vehicle B's turning radius is sharper because it received more positive responses. Given the data, this is a reasonable conclusion, as Vehicle B has a higher number of agreements.

B. "Neither of the claims are correct."

This option contradicts the data, as a significant majority (11 out of 15 for Vehicle A, and 13 out of 15 for Vehicle B) agreed with the manufacturers' claims. Hence, this option can be dismissed.

C. "Only the claim for vehicle B is true because more people agree with their claim."

While it is true that more people agree with the claim for Vehicle B (13 out of 15) compared to Vehicle A (11 out of 15), dismissing the claim for Vehicle A is unjustified given 73.33% (11 out of 15) drivers agreed with it. Therefore, this option is not supported by the available data.

D. "Only the claim for vehicle A is true because 11 out 15 people agree with their claim."

This option dismisses the claim for Vehicle B despite having even stronger support (86.67% agreement). Therefore, this option doesn't align with the data collected.

By analyzing these options, A emerges as the most supported conclusion:

A. Both SUV manufacturers' claims are true, but the turning radius of vehicle B is sharper than the turning radius of vehicle A.

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