Find the best point estimate of the mean salary

Question

Discussion:

(1) Freshman 15 Weight gains.  Based on the sample results, find the best point estimate of the percentage of college students who gain weight in their freshman year.

SEX	WTSEP	WTAPR	BMISP	BMIAP
M	72	59	22.02	18.14
M	97	86	19.7	17.44
M	74	69	24.09	22.43
M	93	88	26.97	25.57
F	68	64	21.51	20.1
M	59	55	18.69	17.4
F	64	60	24.24	22.88
F	56	53	21.23	20.23
F	70	68	30.26	29.24
F	58	56	21.88	21.02
F	50	47	17.63	16.89
M	71	69	24.57	23.85
M	67	66	20.68	20.15
F	56	55	20.97	20.36
F	70	68	27.3	26.73
F	61	60	23.3	22.88
F	53	52	19.48	19.24
M	92	92	24.74	24.69
F	57	58	20.69	20.79
M	67	67	20.49	20.6
F	58	58	21.09	21.24
F	49	50	18.37	18.53
M	68	68	22.4	22.61
F	69	69	28.17	28.43
M	87	88	23.6	23.81
M	81	82	26.52	26.78
M	60	61	18.89	19.27
F	52	53	19.31	19.75
M	70	71	20.96	21.32
F	63	64	21.78	22.22
F	56	57	19.78	20.23
M	68	69	22.4	22.82
M	68	69	22.76	23.19
F	54	56	20.15	20.69
M	80	82	22.14	22.57
M	64	66	20.27	20.76
F	57	59	22.15	22.93
F	63	65	23.87	24.67
F	54	56	18.61	19.34
F	56	58	21.73	22.58
M	54	56	18.93	19.72
M	73	75	25.88	26.72
M	77	79	28.59	29.53
F	63	66	21.89	22.79
F	51	54	18.31	19.28
F	59	62	19.64	20.63
F	65	68	23.02	24.1
F	53	56	20.63	21.91
F	62	65	22.61	23.81
F	55	58	22.03	23.42
M	74	77	20.31	21.34
M	74	78	20.31	21.36
M	64	68	19.59	20.77
M	64	68	21.05	22.31
F	57	61	23.47	25.11
F	64	68	22.84	24.29
F	60	64	19.5	20.9
M	64	68	18.51	19.83
M	66	71	21.4	22.97
F	52	57	17.72	19.42
M	71	77	22.26	23.87
F	55	60	21.64	23.81
M	65	71	22.51	24.45
M	75	82	23.69	25.8
F	42	49	15.08	17.74
M	74	82	22.64	25.33
M	94	105	36.57	40.86

a. Construct a 95% confidence interval estimate of the percentage of college students who gain weight in their freshman year.

b. Assuming that you are a newspaper reporter, write a statement that describes the results. Include all of the relevant information.

(2) NCAA Football coach salaries. A simple random sample of 40 salaries of NCAA football coaches has a mean of $415,953. Assume that o- = $463,364.

a. Find the best point estimate of the mean salary of all NCAA football coaches.

b. Construct a 95% confidence interval estimate of the mean salary of an NCAA football coach.

c. Does the confidence interval contain the actual population mean of $474,477?

(3) Acupuncture for Migraines. In a study designed to test the effectiveness of acupuncture for treating migraines, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for the acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4. The number of migraine attacks for the sham treatment group had a mean of 1.6 and a standard deviation of 1.2.

a. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture.

b. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those given a sham treatment.

c. Compare the two confidence intervals. What do the results suggest about the effectiveness of acupuncture?

(4) Weights of M&Ms lists 100 weights (in grams) of M&M candies. The minimum weight is 0.696 g and the maximum weight is 1.015 g.

Red	Orange	Yellow	Brown	Blue	Green
0.751	0.735	0.883	0.696	0.881	0.925
0.841	0.895	0.769	0.876	0.863	0.914
0.856	0.865	0.859	0.855	0.775	0.881
0.799	0.864	0.784	0.806	0.854	0.865
0.966	0.852	0.824	0.840	0.810	0.865
0.859	0.866	0.858	0.868	0.858	1.015
0.857	0.859	0.848	0.859	0.818	0.876
0.942	0.838	0.851	0.982	0.868	0.809
0.873	0.863			0.803	0.865
0.809	0.888			0.932	0.848
0.890	0.925			0.842	0.940
0.878	0.793			0.832	0.833
0.905	0.977			0.807	0.845
	0.850			0.841	0.852
	0.830			0.932	0.778
	0.856			0.833	0.814
	0.842			0.881	0.791
	0.778			0.818	0.810
	0.786			0.864	0.881
	0.853			0.825
	0.864			0.855
	0.873			0.942
	0.880			0.825
	0.882			0.869
	0.931			0.912
				0.887
				0.886

a. Use the range rule of thumb to estimate o, the standard deviation of weights of all such M&Ms.

b. The 100 weights have a standard deviation of 0.0518 g. Construct a 95% confidence interval estimate of the standard deviation of weights of all M&MS.

c. Does the confidence interval from part b contain the estimated value of o- from part a? What do the results suggest about the estimate from part a?