HYPOTHESIS TESTING

Jan 2006

Step 1: Forming a hypothesis First, form a Null Hypothesis (H0), which

states that the situation is unchanged. This is the mean or statement given in the question, and so is referred to using =, and not >, < or ≠.

For this example, you would write:H0 : μ = 65

You should then form an Alternative Hypothesis (H1), which states that the mean has increased, decreased or just changed. This is referred to using >, < or ≠, and not =. You find this information in the question.

For this example, the key word is underachieving, so they think the mean has decreased. You would write: H1 : μ < 65

Step 2: One- and two-tailed tests Tests involving a > or < are one-tailed as

we are expecting either an increase or a decrease.

Tests involving a ≠ are two-tailed as they consider any change.

For this example, it would be aone-tailed test, as they areexpecting a decrease only.

Step 3: Calculating the test statistic You can now calculate the test statistic using information in

the question, using the formula above.

For this example, we know that: x. = 61.5 μ = 65 σ = 9 n = 35

61.5 65

9

35

= -2.301

Step 4: Significance level The significance level is stated in the

question. Common values used in exam questions are 1%, 5% and 10%.

For this example, the significance level is 5%.

Step 5: Critical region

This is identified by finding critical z-values from Table 4 in the formula book.

For this example, since the significance level is 5%, and it is a one-tailed test, we look up the value for P=0.95 in the table, which is 1.6449.

Since the example talksabout a decrease, we usethe negative critical value.

-1.6449

Step 6: Making your conclusion

You can now make your conclusion based on the context on the question.

If your test statistic falls within the critical region (in green), then you will reject H0, accept H1. If it does not, then you do the opposite.

For this example, the teststatistic (-2.301) doesfall in the critical region,so we would reject H0,accept H1.

-1.6449

-2.301

H0 : μ = 65

H1 : μ < 65

In the context of this question, you could say:“There is significant evidence

at a 5% level of significance to suggest that students are, on average, underachieving.”

Step 7: Errors

You may be asked to identify errors.

There are two types of error: Type I or Type II.

Jan 2007

1. Hypotheses 2. One-tailed or two-tailed 3. Test statistic 4. Significance level 5. Critical region 6. Conclusion

H0 : μ = 30

H1 : μ > 30 One-tailed test Test statistic

x. = 33.5μ = 30σ = 4.25n = 10

1% significance level Critical region Accept H0, reject H1.

“There is insufficient evidence at a 1% level of significance to suggest that the time has been underestimated.”

33.5 30

4.25

10

= 2.60

2.821

2.60