Evidence of the mean waiting time at the main facility

Question

Assignment:

Q1. The data below contains the waiting times in minutes for 15 randomly selected patients at a hospital main emergency room facility and at three satellite facilities.

a. At the .05 level of significance, is there evidence that the mean waiting time at the main facility is more than one hour?

Main	Satellite 1	Satellite 2	Satellite 3
120.08	30.75	75.86	54.05
81.90	61.83	37.88	38.82			Main		Satellite 1		Satellite 2		Satellite 3
78.79	26.40	68.73	36.85
63.83	53.84	51.08	32.83			Mean	69.8427	Mean	41.254	Mean	56.5613	Mean	51.972
79.77	72.30	50.21	52.94			Standard Error	4.69979	Standard Error	5.0065	Standard Error	3.70003	Standard Error	5.21719
47.94	53.09	58.47	34.13			Median	64.99	Median	37.28	Median	58.37	Median	52.94
79.88	27.67	86.29	69.37			Mode	#N/A	Mode	#N/A	Mode	#N/A	Mode	#N/A
48.63	52.46	62.90	78.52			Standard Deviation	18.2022	Standard Deviation	19.3901	Standard Deviation	14.3302	Standard Deviation	20.2061
55.43	10.64	44.84	55.95			Sample Variance	331.32	Sample Variance	375.976	Sample Variance	205.353	Sample Variance	408.286
64.06	53.50	64.17	49.61			Kurtosis	3.21895	Kurtosis	-0.937	Kurtosis	0.30962	Kurtosis	-0.4598
64.99	37.28	50.68	66.40			Skewness	1.42734	Skewness	-0.1182	Skewness	0.24484	Skewness	-0.1506
53.82	34.31	47.97	76.06			Range	72.14	Range	63.31	Range	55.89	Range	72.14
62.43	66.00	60.57	11.37			Minimum	47.94	Minimum	8.99	Minimum	30.4	Minimum	11.37
65.07	8.99	58.37	83.51			Maximum	120.08	Maximum	72.3	Maximum	86.29	Maximum	83.51
81.02	29.75	30.40	39.17			Sum	1047.64	Sum	618.81	Sum	848.42	Sum	779.58
						Count	15	Count	15	Count	15	Count	15
						Confidence Level(95.0%)	10.08	Confidence Level(95.0%)	10.7379	Confidence Level(95.0%)	7.93577	Confidence Level(95.0%)	11.1898

Complete the following:
1. State H0.
2. State H1.
3. State the value of alpha.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. Suppose you use a .01 level of significance instead of a .05 level. Without doing the problem again, would the result be different from that in part (a)? Explain your answer.

Q2. A Wall Street Journal article suggests that age bias is becoming an even bigger problem in the corporate world. In 2001, an estimated 78% of executives believed that age bias was a serious problem. In a 2004 study by ExecuNet, 82% of the executives surveyed considered age bias a serious problem. The sample size for the 2004 study was not disclosed. Suppose 50 executives were surveyed.

a. At the .05 level of significance, is there evidence that the proportion of executives who believed age bias was a serious problem increased between 2001 and 2004?

Complete the following:
1. State H0.
2. State H1.
3. State the value of alpha.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. Explain the meaning of the p-value in this problem.

c. Suppose the sample size used was 1000. Does that change the conclusion you reached in part (a)? How?

d. Discuss the effect that sample size had on the outcome of this analysis and, in general, on the effect sample size plays in hypothesis-testing.

Q3. The data below contains the ratings for food, décor, service, and price per person for a sample of 50 restaurants located in an urban area and 50 restaurants located in a suburban area. At the .05 level of significance, is there evidence of a difference in the mean food rating between urban and suburban restaurants?

Location	Food	Décor	Service	Summated Rating	Location	Cost
Urban	24	21	24	69	0	65
Urban	23	20	20	63	0	48
Urban	18	18	17	53	0	32
Urban	20	18	20	58	0	27
Urban	24	20	23	67	0	47
Urban	19	17	19	55	0	45
Urban	19	18	18	55	0	36
Urban	20	20	20	60	0	55
Urban	21	18	19	58	0	48
Urban	20	15	18	53	0	33
Urban	21	19	20	60	0	45
Urban	20	19	19	58	0	46
Urban	20	17	20	57	0	39
Urban	21	18	19	58	0	44
Urban	19	19	20	58	0	45
Urban	26	26	25	77	0	63
Urban	25	17	22	64	0	54
Urban	20	9	16	45	0	20
Urban	22	18	22	62	0	55
Urban	28	26	27	81	0	73
Urban	24	17	21	62	0	51
Urban	24	18	16	58	0	34
Urban	25	12	19	56	0	28
Urban	25	23	23	71	0	65
Urban	20	17	20	57	0	44
Urban	22	15	21	58	0	43
Urban	25	19	23	67	0	50
Urban	21	11	14	46	0	29
Urban	18	20	19	57	0	33
Urban	19	18	17	54	0	41
Urban	20	17	20	57	0	41
Urban	18	21	19	58	0	52
Urban	23	20	20	63	0	48
Urban	23	20	20	63	0	48
Urban	23	19	20	62	0	38
Urban	23	19	19	61	0	52
Urban	21	14	18	53	0	33
Urban	21	23	17	61	0	40
Urban	19	18	17	54	0	36
Urban	21	19	18	58	0	51
Urban	23	16	21	60	0	39
Urban	19	15	18	52	0	38
Urban	20	12	12	44	0	22
Urban	20	16	18	54	0	35
Urban	19	13	17	49	0	35
Urban	19	14	15	48	0	16
Urban	24	25	23	72	0	74
Urban	22	24	23	69	0	57
Urban	22	22	22	66	0	52
Urban	25	21	20	66	0	68
Suburban	22	17	21	60	1	47
Suburban	18	17	17	52	1	43
Suburban	20	18	18	56	1	44
Suburban	24	19	21	64	1	41
Suburban	22	17	18	57	1	44
Suburban	19	24	18	61	1	48
Suburban	22	20	19	61	1	50
Suburban	21	19	19	59	1	48
Suburban	21	13	19	53	1	38
Suburban	20	18	20	58	1	36
Suburban	15	10	15	40	1	28
Suburban	21	17	21	59	1	25
Suburban	23	18	20	61	1	44
Suburban	25	21	20	66	1	55
Suburban	21	11	15	47	1	20
Suburban	21	16	21	58	1	36
Suburban	23	17	18	58	1	30
Suburban	16	20	17	53	1	44
Suburban	16	17	17	50	1	24
Suburban	25	18	22	65	1	32
Suburban	16	16	12	44	1	29
Suburban	22	15	20	57	1	42
Suburban	23	20	21	64	1	53
Suburban	19	16	18	53	1	27
Suburban	27	22	26	75	1	68
Suburban	22	13	20	55	1	34
Suburban	19	18	20	57	1	30
Suburban	25	11	18	54	1	24
Suburban	25	18	23	66	1	61
Suburban	21	15	17	53	1	34
Suburban	19	26	16	61	1	47
Suburban	22	14	22	58	1	29
Suburban	19	12	15	46	1	26
Suburban	22	17	19	58	1	42
Suburban	24	21	22	67	1	54
Suburban	21	21	17	59	1	51
Suburban	21	14	17	52	1	34
Suburban	22	18	19	59	1	39
Suburban	17	18	17	52	1	39
Suburban	17	23	18	58	1	40
Suburban	20	16	19	55	1	42
Suburban	16	20	17	53	1	40
Suburban	25	21	23	69	1	61
Suburban	21	21	20	62	1	27
Suburban	20	19	18	57	1	37
Suburban	20	16	19	55	1	37
Suburban	19	21	19	59	1	40
Suburban	21	16	20	57	1	39
Suburban	21	17	19	57	1	43
Suburban	19	20	18	57	1	36

Complete the following:
1. State H0.
2. State H1.
3. State the value of alpha.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

Q4. A newspaper article discussed the opening of a Whole Foods Market in the Time-Warner building in New York City. The data below compares the prices of some kitchen staples at the Whole Foods Market and at the Fairway Market located about 15 blocks from the Time-Warner building.

Item	Whole Foods	Fairway
Half-gallon milk	2.19	1.35
Dozen eggs	2.39	1.69
Tropicana orange juice (64 oz.)	2.00	2.49
Head of Boston lettuce	1.98	1.29
Ground round 1lb.	4.99	3.69
Bumble Bee tuna 6 oz. can	1.79	1.33
Granny Smith apples (1 lb.)	1.69	1.49
Box DeCecco linguini	1.99	1.59
Salmon steak 1 lb.	7.99	5.99
Whole chicken per pound	2.19	1.49

a. At the .01 level of significance, is there evidence that the mean price is higher at Whole Foods Market than at the Fairway supermarket?

Complete the following:
1. State H0.
2. State H1.
3. State the value of alpha.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. What assumption is necessary about the population distribution in order to perform the test in (a)?

c. Construct a 99% confidence interval estimate of the difference in price between Whole Foods and Fairway. Do the results of the confidence interval and the hypothesis test agree? Explain.

Q5. As more Americans use cell phones, they question where it is okay to talk on cell phones. The following is a table of results, in percentages, for 2000 and 2006. Suppose the survey was based on 100 respondents in 2000 and 100 respondents in 2006.

Year
OKAY TO TALK ON A CELL PHONE IN A 2000 2006
Bathroom 39 38
Movie/theater 11 2
Car 76 63
Supermarket 60 66
Public transit 52 45
Restaurant 31 21

a. At the .05 level of significance, is there evidence that the proportion of Americans who thought it was okay to use a cell phone in a car in 2000 is significantly greater than the proportion of Americans who thought it was okay to use a cell phone in a car in 2006?

Complete the following:
1. State H0.
2. State H1.
3. State the value of alpha.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. Construct a 95% confidence interval estimate of the difference between the proportion of Americans who thought it was okay to use a cell phone in a car in 2000 and the proportion of Americans who thought it was okay to use a cell phone in a car in 2006. Do the results of the hypothesis test and confidence interval agree? Explain.

Q6. Nine experts rated four brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale (1 = extremely unpleasing, 7 = extremely pleasing) is given for each of the four characteristics: taste, aroma, richness, and acidity. The data below give the ratings for four brands of coffee.

	A	B	C	D
1	24	26	25	22
2	27	27	26	24
3	19	22	20	16
4	24	27	25	23
5	22	25	22	21
6	26	27	24	24
7	27	26	22	23
8	25	27	24	21
9	22	23	20	19

a. At the .05 level of significance, is there evidence of a difference in the mean ratings for the four brands of coffee?

Complete the following:
1. State H0.
2. State H1.
3. State the value of alpha.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. If appropriate, determine which brands differ.

c. One assumption of ANOVA is that the variances of the populations are equal. At the .05 level of significance, is there evidence of a difference in the variation in the ratings of the four brands of coffee?

Complete the following:
1. State H0.
2. State H1.
3. State the value of alpha.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

Q7. The health-care industry and consumer advocates are at odds over the sharing of a patient's medical records without the patient's consent. The health-care industry believes that no consent should be necessary to openly share data among doctors, hospitals, pharmacies, and insurance companies. Suppose a study is conducted in which 600 patients are randomly assigned, 200 each, to three "organizational groupings"-insurance companies, pharmacies, and medical researchers. Each patient is given material to read about the advantages and disadvantages concerning the sharing of medical records within the assigned "organizational grouping." Each patient is then asked, "would you object to the sharing of your medical records with..." and the results are recorded in the cross-classification table below.

Organizational Grouping
OBJECT TO SHARING INFORMATION Insurance Pharmacy Research
Yes 40 80 90
No 160 120 110

Q8. Is there evidence of a difference in the proportions who object to sharing information among the organizational groupings? (Use alpha = .05.)

Complete the following:
1. State H0.
2. State H1.
3. State the value of alpha.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

a. If appropriate, use the Marascuilo procedure and alpha = .05 to determine which groups are different.

Q9. USA Today reported on preferred types of office communication by different age groups. Suppose the results were based on a survey of 500 respondents in each age group. The results are cross-classified in the following table:

Type of Communication Preferred
AGE GROUP Group
Meetings Face-to-Face
Meetings with
Individuals E-mails Other Total
Generation X 180 260 50 10 500
Generation Y 210 190 65 35 500
Boomer 205 195 65 35 500
Mature 200 195 50 55 500
Total 795 840 230 135 2000

At the .05 level of significance, is there evidence of a relationship between age group and type of communication preferred?

Complete the following:
1. State H0.
2. State H1.
3. State the value of alpha.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.