1. A clinic manager conducted an 8-week training on new regulations affecting the practice. Each employee took a pre-assessment and a post-assessment to determine their level of knowledge on the content of the training. The data are in the file "data below."

Individual	Pre	Post
1	2.4	3
2	2.5	2.8
3	3	3.5
4	2.9	3.1
5	2.7	3.5
6	2.7	3.3
7	2.8	3.1
8	3.3	3.8
9	3.2	3.4
10	3	3.8
11	2.1	2.7
12	2.2	2.5
13	2.7	3.2
14	2.6	2.8
15	2.4	3.2

This question has 3 parts.

A)State the null and alternate hypotheses for the study's research question.

B)Conduct a paired t-test at the 0.05 level of significance and report your findings.

C) Is this a two-tailed or one-tailed test? Explain your choice.

1. As part of some ongoing research related to the relationship between smoking and other health decisions, researchers studies the link between the number of cigarettes smoked per day and the BMI of participants. The data are shown below.

Number of cigarettes	BMI
24	27
21	29
19	31
10	22
18	23
39	25
22	26
24	2
26	28
27	31
17	29
13	22
23	23
25	27
21	24
34	32
21	28
36	29
21	23
12	26
17	22
18	24
22	24
25	24

This question has 3 parts.

A)Discuss the correlation between the two variables, including its significance.

B)What does the value of r² represent in correlation and regression?

C)Conduct a simple linear regression where the number of cigarettes is the independent variable and the BMI is the dependent variable.

1. What is the regression equation?
2. What does the regression equation tell us?
3. Using the output from Excel, explain the standard error and the residual plot.
4. Considering the overall information you see, would you suggest this is a good regression model for predicting BMI from the number of cigarettes smoked per day?

Q. Researchers studies the effect of lengths of time of therapy and time of day of therapy on patients. In the file "(data below)," the scores are number of visits to dismissal.

Time	Short	Moderate	Long
Early	28	35	32
	19	22	29
	32	33	16
	15	21	18
	13	17	20
Mid AM	39	36	37
	12	38	40
	42	44	18
	25	27	28
	21	22	36
Mid PM	44	42	35
	21	17	39
	38	31	41
	32	29	31
	29	37	34
Late	17	18	22
	12	27	25
	23	15	14
	19	29	16
	14	16	19

This question has 3 parts.

A)Write the null and alternate hypotheses for the ANOVA.

B)What does it mean when we set the value of alpha to 0.05? What are we actually doing (or saying)?

C)Conduct a two-way ANOVA on the data and report your findings.

Q. A researcher was doing a study on how well a call center response plan was being utilized by a group of patients. In the data below, the number of calls is shown in column A, and the number of incidents is shown in Column B. We can take the number of incidents to be the expected value for the data. A nice easy-to-use calculator can be found at https://www.socscistatistics.com/tests/goodnessoffit/default2.aspx.

Socioeconomic Class	Calls	Incidents
A	5	9
B	21	16
C	34	27
D	42	48
E	25	27

This question has 3 parts.

1. Why do we use chi-square and other non-parametric tests for some data?
2. Conduct a chi-square goodness-of-fit test to the data and report your results.
3. In statistics we often discuss a Type I error. What does it mean if we have observed a Type I error?