Question

As you are answering each question, please explain your answers in addition to picking what you believe to be the correct letter choice.

1. Which of the following does not need to be known in order to determine the p-value?

1. the significance (or alpha) level
2. knowledge of whether the test is one-tailed (or one-sided) or two-tailed (or two-sided)
3. the value of the test statistic
4. All of the above need to be known to determine the p-value.
5. None of the above need to be known to determine a p-value.

2. You conduct a hypothesis test with a sample of size n = 40 and you observe values for the sample mean and sample standard deviation that do not lead to the rejection of the null hypothesis. In fact, you determine the p-value is 0.0667. What would you expect to happen to the p-value if the sample size was smaller? Assume here the sample mean and sample standard deviation would not change with the smaller sample size.

1. The p-value would stay the same
2. The p-value would increase (or get bigger)
3. The p-value would decrease (or get smaller)
4. This cannot be answered since p-values are not affected at all by sample size

3. If a p-value is smaller than the alpha level, what does this mean?

1. The results are practically important.
2. The null hypothesis does not provide a plausible explanation for the findings.
3. The null hypothesis is definitely false.
4. The alternative hypothesis is definitely true.
5. All of the above.

4. Which one of the following statements about p-values is correct?

1. If the p-value for a hypothesis test is 0.15, this means the probability that the null hypothesis is false is 0.15.
2. If a p-value is 0.04 and the alpha-level is 0.01, our decision should be to fail to reject the null hypothesis.
3. A p-value that is less than 0 means that we have an outcome that is extremely rare.
4. The smaller the p-value, the more evidence there is in favor of the null hypothesis.  
5. All of the above statements are correct.  

5. Imagine you have data in the form of means, and you have conducted a hypothesis test. You obtain a p-value of 0.0001. Which of the following statements must be true regarding this p-value?

1. The difference between µ and x must be huge.
2. Since the p-value is so small, the results will have practical importance as well as statistical significance.
3. The sample standard deviation, or s, must be very small.
4. All of the above.
5. None of the above.

Answer 1

1.significance level (P value = Prob( T> To| Ho)

Where T is test statistic and To is observed value of test statistic. So we do not need significance level.)

2. The p-value would stay the same. (When null hypothesis is true, P value does not change as it does not depend on n)

3. The null hypothesis is definitely false. (Because smaller p value supports alternative hypothesis.)

4. Option B. (The decision rule is if l. O. S > p-value, we should reject Ho)

5. None of the above.