Question

Calculate a 90% confidence interval estimate for time (minutes) it takes to fill out form 4 by all people. Interpret your result. g) Assuming 102 minutes for population mean time for filling all forms and a standard deviation of 8 minutes. Design, conducts and conclude a hypothesis test that shows the mean time of filling form 1 differs from population mean. Interpret your result using both p-value and critical value approach. Alpha=0.05 h) Suppose, IRS is interested in the difference between the population mean of form 4 and 2. Develop a 90% confidence interval of the difference between the two population means. Can we conclude, using 0.05 level of significance that the population mean time of form 4 is greater than population mean time of form 2? Calculate and interpret your results. (hint: you can use the template in chapter 10 to calculate degrees of freedom and the standard error) i) Assuming individuals are not homogenous, can IRS assume that there are differences between the four types of forms at 1% significance level? Conduct the test hypothesis, interpret your result and make a conclusion out of your analysis.

1	109	115	126	120
2	98	103	107	108
3	29	27	53	38
4	93	95	103	109
5	62	65	67	64
6	103	107	111	128
7	83	82	101	116
8	122	119	141	143
9	92	101	105	108
10	107	113	127	113
11	103	111	111	108
12	54	64	67	62
13	141	145	142	160
14	92	94	95	102
15	29	32	33	62
16	83	83	89	86
17	34	36	40	48
18	83	86	90	119
19	157	157	172	193
20	99	107	111	100
21	118	123	117	130
22	58	65	75	81
23	66	71	79	81
24	60	60	78	41
25	102	106	100	142
26	128	134	135	142
27	87	93	90	77
28	126	134	129	154
29	133	130	148	164
30	100	112	107	120

Answer 1

The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

	Mean	n	Std. Dev
	91.7	30	32.22	Group 1
	95.7	30	32.57	Group 2
	101.6	30	31.88	Group 3
	107.3	30	38.17	Group 4
	99.1	120	33.91	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	4,206.09	3	1,402.031	1.23	.3033
Error	1,32,606.23	116	1,143.157
Total	1,36,812.33	119

The p-value is 0.3033.

Since the p-value (0.3033) is greater than the significance level (0.01), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there are differences between the four types of forms.

Tukey Simultaneous Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
C2 - C1	3.97	8.73	(-18.81, 26.74)	0.45	0.969
C3 - C1	9.93	8.73	(-12.84, 32.71)	1.14	0.667
C4 - C1	15.60	8.73	(-7.18, 38.38)	1.79	0.285
C3 - C2	5.97	8.73	(-16.81, 28.74)	0.68	0.903
C4 - C2	11.63	8.73	(-11.14, 34.41)	1.33	0.544
C4 - C3	5.67	8.73	(-17.11, 28.44)	0.65	0.916

Individual confidence level = 98.97%