Question

Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

Claim: The mean age of students in a large math class is less than 35. A simple random sample of the students has a mean age of 17.3.

Choose the correct answer below.

A. The sample is unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.

B. The sample is unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.

C. The sample is not unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.

D. The sample is not unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim

Answer 1

Rare event rule : - We make an assumption

we find probability

If probability is low, our assumption is low.

Now,

Mean age < 35

Sample mean age = 17.3

So, if claim is true, sample is not unusual.

claim is false, sample is unusual

so, sufficient evidence to support the claim

we find probability

If probability is low, our assumption is low.

Now,

Mean age < 35

Sample mean age = 17.3

So, if claim is true, sample is not unusual.

claim is false, sample is unusual

so, sufficient evidence to support the claim

a.there isn't sufficient evidence to support this claim, because the coin is a fair coin