Question

Please answer the following questions based on the analysis in excel.

1. Calculate the mean, standard deviation, and variance of the two samples. Embed the answers in the data sheet.

2. Calculate the degrees of freedom for a t test assuming the population standard deviation is unknown with unequal variance between samples.

3. Perform a two-tailed two-sample mean test assuming the population standard deviation is unknown with unequal variance. (.01 significance level)

4. State your conclusion from the two-tailed test.

M car	J car
31	27
30	29
29	27
30	28
33	28
36	29
31	30
29	28
28	30
34	25
26	27
32	25
28	28
28	26
32	24
28	25
33	31
33	28
28	26
27	28
35	25
30	28
26	27
31	28
	27
	26
	28
	25

Answer 1

Excel output:

M car	J car			M car	J car
31	27		Mean	30.33333	27.25
30	29		Variance	7.623188	3.009259
29	27		Std. dev	2.761012	1.734722
30	28
33	28
36	29		t-Test: Two-Sample Assuming Unequal Variances
31	30
29	28			Variable 1	Variable 2
28	30		Mean	30.33333	27.25
34	25		Variance	7.623188	3.009259
26	27		Observations	24	28
32	25		Hypothesized Mean Difference	0
28	28		df	38
28	26		t Stat	4.729026
32	24		P(T<=t) one-tail	1.54E-05
28	25		t Critical one-tail	1.685954
33	31		P(T<=t) two-tail	3.08E-05
33	28		t Critical two-tail	2.024394
28	26
27	28
35	25
30	28
26	27
31	28
	27
	26
	28
	25

You can use following functions and test to find answer:

Mean: =average()

variance: =var()

standard deviation: =stdev()   

Now use " t test: two sample Assuming unequal variance test " to find degrees of freedom, p value

1.

	M car	J car
Mean	30.33333	27.25
Variance	7.623188	3.009259
Std. dev	2.761012	1.734722

2.

Degrees of freedom = 38

3.

test statistics =t = 4.729026

p value = 0.0000308

4.

Since p value is smaller than 0.05 we reject null hypothesis of equal mean at 5 % level of significance and conclude that two population means are significantly different.