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. 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

2. 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.

3. 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)

The p-value would increase (or get bigger) (since standard error will become large and therefore test statsitic become small)

2)

A.The results are practically important.

3)

B.Since the p-value is so small, the results will have practical importance as well as statistical significance.