Question

Requirements and Conclusions Are any of the three requirements violated? Can the methods of this section be used to test the claim? It was stated that we can easily remember how to interpret P-values with this: "If the P is low, the null must go." What does this mean? Another memory trick commonly used is this: "If the P is high, the null will fly." Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading? Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like 0.0483?

Answer 1

For part B, the complete question is;

Use these results from a USA Today survey in which 510 people chose

to respond to this question that was posted on the USA Today website: "Should Americans

replace passwords with biometric security (fingerprints, etc)?" Among the respondents,

53% said "yes." We want to test the claim that more than half of the population believes that

passwords should be replaced with biometric security. Another memory trick commonly used is this: "If the P value is high, the null will fly." Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how

is this memory trick misleading?

Answer:

Explained below.

Step-by-step explanation:

A) We are told to explain "If the P is low, the null must go"

What this means is that if the p-value is less than the significance level, we reject the null hypothesis!

B) We want to explain the statement;"If the P is high, the null will fly."

Now, what this means is that if the p-value is is larger than the significance level, we will fail to reject the null hypothesis.

Thus, the memory stick may be misleading because the statement "the null will fly" may imply that we have accepted the null hypothesis whereas we only failed to reject it!

C) It would not be unwise to use a significance level of 0.0483 because there is no proven reason why 0.01 and 0.05 are better.

Another reason is that in binomial probability distribution, the p-value at significance levels of 0.01 and 0.05 may not be gotten whereas it may be gotten if we use 0.0483.