Marital Status	Age	CholChange	BPChange	VisionChange	Happy1	Happy2	Happy3	Male?			Patients on anti-smoking medication for twelve weeks tested for side effects
S	55	1.7	-1	-2	39	42	47	Y
M	53	6.4	5	5	26	35	38	N			Marital Status:
M	37	-2.85	0	-2	59	64	72	N				M = married
DWS	42	-1.8	0	0	67	66	71	Y				S = Single
S	41	-2.85	-4	0	26	33	40	N				DWS = Divorce, Widowed, or Separated
M	67	-2.9	-4	-1	28	27	26	Y			Happy 1, 2, and 3
S	65	-2.4	0	-1	44	44	47	N				Score between 1 and 100 on a happiness test. Test given three times.
M	61	-2.2	-2	6	38	46	54	Y					Time 1: before medication began
S	44	-1.15	1	2	34	35	34	Y					Time 2: after six weeks of medication
S	59	-0.65	1	2	63	70	75	N					Time 3: after twelve weeks on medication
DWS	40	4.25	1	-2	48	52	53	N			CholChange
M	64	0.25	5	4	37	41	47	Y				Change in patient's cholesterol between beginning and end of the twelve weeks
M	40	-4	-7	4	48	50	55	N			BP Change
M	45	-1.8	2	0	69	74	76	N				Change in patient's systolic blood pressure between beginning and end of the twelve weeks
S	50	-1.65	-1	0	64	70	72	Y			Vision Change
M	50	2.95	3	-4	62	66	75	Y				Change in patient's score on a vision test between beginning and end of the twelve weeks. Higher scores represent better vision.
M	45	-1.3	1	2	47	47	51	N			Age
S	60	7.5	9	6	55	58	62	N				Age at beginning of study, in years
DWS	29	3.6	3	-2	35	43	43	Y			Male?
S	38	7.4	5	2	42	41	51	Y				"Y" if the patient is male, and "N" otherwise.
DWS	56	-1.75	0	-1	55	57	63	Y
DWS	53	-1.15	1	-2	38	43	50	Y
M	60	1.75	3	-1	60	59	64	N
S	51	6.6	4	-2	69	68	69	N
S	68	-2.2	1	3	32	39	41	N
M	62	6.4	6	0	30	35	41	Y
M	49	-1.7	-2	9	35	39	37	Y
S	50	-1.35	-3	-3	36	45	42	Y
S	59	2.75	3	4	36	38	43	Y
S	36	-3.15	-5	5	60	63	64	Y
S	43	0.1	3	6	48	57	60	N
M	50	-4.25	-3	0	56	58	68	N
S	28	4.5	4	0	55	57	57	N
M	47	-2.25	-3	3	59	60	60	Y
M	49	-0.15	3	-4	43	46	50	Y
DWS	55	0.5	4	5	44	47	51	N
M	59	-2	-3	1	30	38	41	Y
M	58	-2.3	-3	6	59	66	69	N
DWS	39	-4.2	-8	0	57	65	72	Y
M	50	1.65	0	7	43	51	56	N
M	67	-0.4	2	-2	50	54	55	N
S	46	-2.65	1	3	40	41	41	Y
DWS	50	4.7	5	-4	62	67	66	Y
M	52	-2.55	-5	1	58	58	58	N
S	34	-0.25	0	8	45	52	59	N
S	40	6.6	9	2	48	54	57	Y
S	30	3.3	5	6	33	37	45	N
S	59	2.95	3	6	37	44	46	N
M	39	-3.65	-2	-2	49	58	62	N
M	66	4.95	3	-4	59	62	67	N
S	62	4.3	6	8	41	37	47	Y
M	31	3.35	5	2	46	51	52	Y
M	53	2.5	4	-5	46	50	52	Y
M	53	4.35	2	0	67	70	79	N
M	63	4.05	3	2	39	39	44	Y
DWS	52	-3.35	-1	4	75	82	86	Y
M	45	3.9	7	-7	62	64	71	Y
DWS	47	-3.45	-3	-5	40	48	48	N
S	62	-4.45	-4	4	51	58	66	N
DWS	41	-2.9	-1	6	66	74	71	N
DWS	55	-0.25	-1	4	35	38	41	N
M	45	6.3	9	4	50	54	56	N
M	46	-0.3	1	-4	37	36	43	N
M	49	5.95	7	0	49	52	59	N
DWS	43	-0.3	1	3	51	58	63	N
DWS	61	4.55	3	-1	33	38	40	Y
S	48	5.55	3	7	41	44	50	N
DWS	65	-3.65	-5	3	58	66	69	Y
DWS	63	6.45	9	6	33	31	36	Y
M	23	1.8	4	3	42	41	48	Y
DWS	46	-0.05	1	-5	44	48	56	N
M	62	6.15	6	2	55	53	51	N
M	45	-0.85	0	-2	42	45	49	Y
S	60	5.6	7	-2	24	29	29	Y
S	60	2.05	4	-2	81	84	87	Y
M	51	-2.45	-1	-1	40	44	49	Y
M	43	3.25	2	6	67	72	72	N
M	63	5.85	5	3	65	63	67	Y
M	62	-1.35	-4	3	27	31	38	N
M	51	7.1	9	5	49	54	57	N
S	58	5.65	4	1	45	43	41	Y
M	70	0.65	1	2	33	44	46	Y
M	66	6.05	6	-2	43	49	48	N
M	62	1.3	1	0	35	43	51	N
M	48	-3.7	-6	-4	46	44	50	N
M	44	3.15	5	-3	53	55	65	Y
M	68	6.1	6	0	40	47	46	N
DWS	41	-1.9	1	-2	62	68	72	N
M	55	6.15	6	2	68	72	76	Y
DWS	60	-1.6	2	6	68	79	84	Y
M	56	-4	-1	1	58	63	66	Y
DWS	61	5.6	5	7	65	64	63	Y
S	47	2.15	1	1	33	36	36	N

Drug Trial data - Use the Happy1 variable.Suppose someone claims the population mean is 55 and the standarddeviation is 10.

PART 1 - Sampling Distribution Exercises

For now, assume both of the claims about the population are correct.

1a. Given the assumed pop. mean and st.dev, calculate the probability of observing a value above the number for your first data point in your file. 1b. Suppose you collected 8 new data points in a new sample. Calculate the probability that the mean of these 8 new data points is above the number for your first data point in your file. 1c. If this is a normally distributed variable, above what value should you find 70% of data points? How many of the values from your data set are above this value? 1d. If this is a normally distributed variable, between what two numbers (centered around the assumed mean) should you find 68% of data points? What percentage of your data points are between these numbers? 1e. Think about your answers to 1c and 1d. Does this variable appear to be normally distributed with this mean and standard deviation?

PART 2 - Suppose you are now suspicious of both claims about the population. Therefore, you disregard those claims and depend on estimates of the mean and standard deviation from your sample.

2a. Describe the sample and population you are studying with this data. (This is not given in the data, you have to make up a story about who or what you are studying.) 2b. Calculate the sample mean and sample standard deviation for your variable. Keep at least four decimal places 2c. Calculate the standard error and the margin of error for a 90% confidence interval. Keep at least four decimal places. 2d. Combine these three responses to calculate and interpret a 90% confidence interval for the population mean. Use the format: "The mean of XXX is ###. Therefore I believe the mean of YYY is probably around ###. I am 90% confident that ______."

PART 3 - Make a confidence interval for a proportion. Drug Trial Data - Investigate the proportion of married patients.

3a. What is a reason why you would want to estimate this population proportion. What can be learned? 3b. State the sample size, n, and the sample proportion, "p bar" (p with a line over it). 3c. Calculate a 95% confidence interval for the population proportion,p. Report at least four decimal places. 3d. Interpret this interval in the same way you did in step 2d.