Make a decision about the given claim. Use only the rare event rule, and make su

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 respiration rate (in breaths per minute) of students in a large statistics class is less than 32. A simple random sample of the students has a mean respiration raterespiration rate of 14.3.

Explanation / Answer

Question 1:

Under the rare event rule if the probability of an event occuring is too small, then that event is not so probable. Here we have the null hypothesis that the coin is fair and the alternate event is that the coin favors head. As the proportion of heads in 20 tosses is 0.55 which is very close to 0.5, according to the intuitive rare event rule, the null hypothesis cannot be rejected here and we dont have sufficient evidence to claim that the coin favors the head.

Question 2:

Here as the sample mean of the students respiration raterespiration rate is way lower than 32, according to the rare event rule, it has a very low probability that the mean of the random sample comes out to be so low equal to 14.3 therefore we dont have enough evidence to go with the fact that the mean is 32.

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