Statistics - Hypothesis Testing

copy_of_testing_data.xlsx

Sheet1

Performance before training	Perfomance after training
65	70	T-test
87	88
23	30		t-Test: Two-Sample Assuming Unequal Variances
45	49
67	68			Performance before training	Perfomance after training
90	94		Mean	53.4545454545	57.3636363636
24	30		Variance	789.2727272727	726.2545454545
45	48		Observations	11	11
31	36		Hypothesized Mean Difference	3.909090909
19	23		df	20
92	95		t Test	-0.6660705479
53.4545454545	57.3636363636		P(T<=t) one-tail	0.2564881022
			t Critical one-tail	1.7247182429
			P(T<=t) two-tail	0.5129762044
Main difference	3.9090909091		t Critical two-tail	2.0859634473
			t Test
			the p-value is greater than alpha at α=95% confidence level therefore we accept the null hypothesis
			that the training was effective
		ANOVA
			Anova: Single Factor
			SUMMARY
			Groups	Count	Sum	Average	Variance
			Performance before training	11	588	53.4545454545	789.2727272727
			Perfomance after training	11	631	57.3636363636	726.2545454545
			ANOVA
			Source of Variation	SS	df	MS	F	P-value	F crit
			Between Groups	84.0454545455	1	84.0454545455	0.1109124937	0.7425735112	4.3512435033
			Within Groups	15155.2727272727	20	757.7636363636
			Total	15239.3181818182	21
		Chi-Square
			The chi-square of the given data
			0.8639758036
			Training was effective since the p value is greater than α=0.05% confidence level