Section 3: Case Studies of Null Hypothesis Testing.

## Question 10

You are running a series of statistical tests in SPSS using the standard criterion for rejecting a null hypothesis. You obtain the following *p* values.

Test 1 calculates group differences with a *p* value = .07.

Test 2 calculates the strength of association between two variables with a *p* value = .50.

Test 3 calculates group differences with a *p* value = .001.

For each test below, state whether or not you reject the null hypothesis. For each test, also explain what your decision implies in terms of group differences (Test 1 and Test 3) and in terms of the strength of association between two variables (Test 2).

Test 1 (group differences) = you do not reject the null hypothesis. This does not mean the null is true since .07 >.05. The results are 7% of the time.

Test 2 (strength of association) = Failed to reject the null hypothesis.

Test 3 (group differences) = Reject the null hypothesis.

## Question 11

A researcher calculates a statistical test and obtains a *p* value of .86. He decides to reject the null hypothesis. Is this decision correct, or has he committed a Type I or Type II error? Explain your answer.

[It will rely upon the level of significance of the test. On the off chance that p-value is ≥ level of significance α, at that point the choice ought to be not to reject the null hypothesis. On the off chance that null is rejected at such circumstances, type I error is submitted. In the event that p-value is < level of significance α, the choice ought to be to reject the null hypothesis. If the null is not rejected at such circumstances Type II error is submitted.]

## Question 12

You are proposing a research study that you would like to conduct while attending Capella University. During the proposal, a committee member asks you to explain in your own words what you meant by saying “*p* less than .05.” Provide an explanation.

[The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event.

So, if a P-value is too low, meaning it is less than a particular critical point, which is .05 here, we reject null hypothesis. Because the probability of that certain event occurring is very low.]