Application Questions:

The previous Statistics classes at Delta State were required to take the Big Five Personality Inventory to predict success in the course. The previous courses openness scores gave the following descriptive statistics: =5.4 and =1.3. You are going to try to determine if your current class sample's (n=10) openness mean is statistically significantly different from the previous semesters' scores.

1.Step 1-State Hypotheses:

a.Null hypothesis (remember, this is the villain who doesn't believe in you):

b.Alternative hypothesis:

c.Would you use a one-tailed or two-tailed test?

2.Step 2- Set Decision Criterion:

a.Choose your level (your critical region):

3.Step 3- Make Up Data for your Sample's openness score:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

4.Step 4- Calculate Statistics (show your work!):

a.What is your sample mean:

b.Compute standard error (pg. 178):

c.Run a z-test to get your new z-score(pg. 183):

d.Is your z-score in the critical region? (is it greater than 1.96 or less than -1.96)

5.Step 5- Make a Decision:

a.Do you reject or retain the null hypothesis (is it in the critical region)? (Does evil win?)

b.What does that mean about your sample's score on openness compared to previous semesters?

Conceptual Questions:

1.Let's say you used a sample size of n=40 for previous experiment. What would that change in your results?

When a sample size is 40, the sample size is large. Then even though population variance is unknown, the statistic has a normal district distribution refusing sample variance as a substitute. Therefore, no it would not change the results.

2.What are the pros and cons of running a two-tailed test?

The advantage of using a two-tailed hypothesis is that you can detect both the positive and negative effects it is also standard in scientific research where discovering any type of effect usually of interest to the researcher. However, it has less statistical power to detect on effect in one direction than one tail hypothesis test with the same design and significant level.

3.When we are conducting a one-sample z test why do we factor in standard error? What could happen if we didn't?

When conducting a one sample the test we factor in standard error because it allows us to calculate the probability occurring within our normal district distribution. If this is not when solving for each one sample the test then there will not be link to any of your data set since it is not considering

4.If a study claims to have a low standard error, what does that mean conceptually (don't just put the definition of standard error J)