Fred wanted to test the claim that 90% of all automobile tires are underinflated

Question

Fred wanted to test the claim that 90% of all automobile tires are underinflated. He collected a random sample of 10 automobile tires and 9 were underinflated, and then he did all the numerical calculations correctly, However, his statistics professor told him that the data that he collected were insufficient. Why? Answer the following riddle: A lane cowboy rode into Dodge City and stayed just two days. The cowboy said "I rode in on Tuesday, cleaned up the town, and then left two days later on Tuesday." Assuming she is telling the truth, how is this possible?

Explanation / Answer

A) Fred's sampling was a random one out of a very tiny proportion of the actual number of automobiles. In order to prove the claim that 90% of all automobile tires are underinflated, he needs to collect a random sample of a vast majority of autombiles and the results need to be well in excess of the 90% as per the claim.

B) Possible answers:

i) A cowboy is a male. "She is telling the truth" implies this is some girl speaking. As a result the actual statement made is something different.

ii) "Tuesday" is the name of the cowboy's mount and not the day of the week. The cowboy said " I rode in on Tuesday, cleaned up the town, and then left two days later on Tuesday". This means one (or both) of the Tuesdays he is referring to is his mount.

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