Introductory Statistics Exam: Solutions To Four Questions

Examination scores		Classes	Frequency	Cumulative Frequency	Relative Frequency	Cumulative Relative Frequency	Percent Frequency
52		> 57	2	2	0.1	0.1	10%
63		57 to 61	1	3	0.05	0.15	5%
92		61 to 66	2	5	0.1	0.25	10%
90		66 to 71	0	5	0	0.25	0%
99		71 to 76	4	9	0.2	0.45	20%
72		76 to 80	2	11	0.1	0.55	10%
58		80 to 85	1	12	0.05	0.6	5%
75		85 to 90	3	15	0.15	0.75	15%
92		90 to 94	2	17	0.1	0.85	10%
76		< 94	3	20	0.15	1	15%
65		Total	20	99	1	4.95	1
74
86
95
79
56
84
88
80
99

ANOVA
	df	SS	MS	F	Significance F
Regression	1	354.689	354.689	1.966	0.169
Residual	39	7035.262	180.391
	40	7389.951

	Coefficients	Standard error	t stat	P value
Intercept	54.076	2.358	22.933	0.001
X	0.029	0.021	1.381	0.175

Employee’s output for a day’s work
Program A	Program B	Program C	Program D
150	150	185	175
130	120	220	150			Anova: Single Factor
120	135	190	120
180	160	180	130			SUMMARY
145	110	175	175			Groups	Count	Sum	Average	Variance
						Program A	5	725	145	525
						Program B	5	675	135	425
						Program C	5	950	190	312.5
						Program D	5	750	150	637.5


						ANOVA
						Source of Variation	SS	df	MS	F	P-value	F crit
						Between Groups	8750	3	2916.667	6.140	0.006	3.239
						Within Groups	7600	16	475

						Total	16350	19

Weekly sales data
Week	Price	Advertising	Sales
1	0.33	5	20				SUMMARY OUTPUT
2	0.25	2	14
3	0.44	7	22				Regression Statistics
4	0.4	9	21				Multiple R	0.8778
5	0.35	4	16				R Square	0.7706
6	0.39	8	19				Adjusted R Square	0.6558
7	0.29	9	15				Standard Error	1.8374
							Observations	7

							ANOVA
								df	SS	MS	F	Significance F
							Regression	2	45.3528	22.6764	6.7168	0.0526
							Residual	4	13.5043	3.3761
							Total	6	58.8571

								Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
							Intercept	3.598	4.052	0.888	0.425	-7.653	14.848	-7.653	14.848
							Price	41.320	13.337	3.098	0.036	4.290	78.350	4.290	78.350
							Advertising	0.013	0.328	0.040	0.970	-0.896	0.923	-0.896	0.923

							SUMMARY OUTPUT

							Regression Statistics
							Multiple R	0.8778
							R Square	0.7705
							Adjusted R Square	0.7246
							Standard Error	1.6438
							Observations	7

							ANOVA
								df	SS	MS	F	Significance F
							Regression	1	45.3473	45.3473	16.7831	0.0094
							Residual	5	13.5098	2.7020
							Total	6	58.8571

								Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
							Intercept	3.58	3.61	0.99	0.37	-5.69	12.86	-5.69	12.86
							Price	41.60	10.16	4.10	0.01	15.50	67.71	15.50	67.71

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