Question

I am stuck on these problems and need a explanation as to why i keep getting them wrong/ what the answer is

H₀:  ₁ -  ₂= 0
H_a:  ₁ -  ₂≠ 0

The following results are from independent samples taken from two populations.

Sample 1	Sample 2
n 1 = 35	n 2 = 40
x 1 = 13.6	x 2 = 10.1
s 1 = 5.8	s 2 = 8.2

a. What is the value of the test statistic (to 2 decimals)?

b. What is the degrees of freedom for the t distribution? (Round down your answer to the whole number)

Answer 1

Test and CI for Two Variances

Method

Null hypothesis Sigma(1) / Sigma(2) = 1
Alternative hypothesis Sigma(1) / Sigma(2) not = 1
Significance level Alpha = 0.05

Statistics

Sample N StDev Variance
1 35 5.800 33.640
2 40 8.200 67.240

Ratio of standard deviations = 0.707
Ratio of variances = 0.500

Test
Method   DF1 DF2 Statistic P-Value
F Test (normal) 34 39 0.50 0.042

Since p-value<0.05 so we can't assume that two populations have same variance. So we perform 2 sample t test with unequal variances.

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 35 13.60 5.80 0.98
2 40 10.10 8.20 1.3

Difference = mu (1) - mu (2)
Estimate for difference: 3.50
T-Test of difference = 0 (vs not =): T-Value = 2.15 P-Value = 0.035 DF = 70

a. Value of test statistic=2.15

b. The degrees of freedom for the t distribution=70.