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Question 1. (8pts)

The age (in years) of a sample of 20 motor cyclists killed in road traffic accidents is given below:

18	41	24	28	71	52	15	20	21	31
16	24	33	44	20	24	16	64	24	32

(i)	Draw a histogram. Is the distribution symmetric or skewed?
(ii)	Calculate the mean, median, and mode.
(iii)	Calculate the range, inter quartile range, and standard deviation. Which of these is better to
	describe the variability of these data?
(iv)	Calculate the confidence interval.

Question 2. (7 pts)

The table below shows the height of 12 fathers and their fully grown sons:

Father's Height (cm)	Son's height (cm)
190	189
184	186
183	180
182	179
179	187
178	184
175	183
174	171
170	170
168	178
165	174
164	165

(i)	Draw a scatter plot of father's height versus son's height
(ii)	From the graph, does there appear to be a relationship between the two variables?

Question 3 (6 pts)

The table below shows the results of a randomized, double-blind, placebo-controlled trial
examining whether patients with chronic fatigue syndrome (CFS) improved
6 weeks after treatment with intramuscular magnesium. The group who received the magnesium
were compared to a group who received a placebo and outcome was feeling better.

Do these data suggest that the magnesium-treated CFS patients have different outcomes to placebo-treated patients after 6 weeks of treatment?
What is the Chi square result?

Treatment		Outcome
	Felt Better	Did Not Feel Better	Total
Magnesium	12	3	15
Placebo	3	14	17
Total	15	17	32

H0	No difference in outcomes, proportion of CFS, patients feeling better at 6 weeks between the magnesium and placebo treated groups
H1	There is a difference in outcomes, proportion of CFS, patients feeling better at 6 weeks between the magnesium and placebo treated groups

Question 4 (6 pts)

Two physicians examined results of 50 randomized, double-blind, placebo-controlled trial
examining whether patients with chronic fatigue syndrome (CFS) improved
6 weeks after treatment with intramuscular magnesium. The group who received the magnesium
were compared to a group who received a placebo and outcome was feeling better.
Physician A believed 15 patients received magnesium as opposed to placebo. Physician B believed
20 patients received magensium as opposed to placebo. They both agreed on 9 patient cases having received magnesium as opposed to placebo. What is the Chi square result?

Treatment		Outcome
	Physician B - Magnesium	Physician B - Placebo	Total
Physician A - Magnesium	9	?	15
Physician A - Placebo	?	?	?
Total	20	?	50

Question 5. (6pts)

A researcher at SRVMC wishes to try three different techniques to lower the blood pressure of individuals diagnosed with high blood pressure. The subjects are randomly assigned to three groups.

Group 1 takes medication

Group 2 exercises

Group 3 follows a special diet.

After four weeks, the reduction in each person’s blood pressure is recorded. At an alpha level of significance of 0.05, the researchers now must test the claim that there is no difference among the means.

Medication	Exercise	Diet
10	6	5
12	8	9
9	3	12
15	0	8
13	2	4

Is he correct? Run the appropriate test to determine if he is correct.

Question 6. (7 pts)

Medical Rehabilitation Education Foundation found the average cost of rehab for stroke victims is $24,672. Is this average wrong, outdated—is the cost at other area local hospitals different than the average? A Researcher selects 35 random stroke patients and finds an average cost of $25,226 with a σ = $3251 At α = 0.01, can it be concluded that the cost of an average stroke rehab is different than the originally assumed $24,672?