Question

3. Perform a hypothesis test for Ho: ui Sul vs. Hi: ui > 2. The sample sizes are ni = 10 and n = 15, sample means are Xi=44.7 and that X2=53.8 and sample standard deviations are si = 11 and 52 = 6. Perform the test assuming variances are unequal. Use 5% significance.

Answer 1

Solution:

Here, we have to two sample t test for difference in two population means.

H₀: µ₁ = µ₂ versus H_a: µ₁ > µ₂

This is an upper tailed test.

The test statistic formula for two sample t test for mean assuming unequal population variances is given as below:

t = (X1bar – X2bar) / sqrt[(S₁² / n₁)+(S₂² / n₂)]

Degrees of freedom = [(S₁²/n₁) + (S₂²/n₂)]^2 / [((S₁²/n₁)^2/(n₁ – 1)) + ((S₂²/n₂)^2/(n₂ – 1))]

We are given

X1bar = 44.7

S1 = 11

n1 = 10

X2bar = 53.8

S2 = 6

n2 = 15

t = (44.7 – 53.8)/sqrt[(11^2/10)+(6^2/15)]

t = -2.3898

df = 12

(by using excel)

P-value = 0.9829

(by using t-table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis