Question

Provided below are summary statistics for independent simple random samples from two populations. Use the nonpooled t-test and the nonpooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. X = 11, S, = 5, n = 25, X2 = 10, S2 = 9, n2 = 20 a. Right-tailed test, a = 0.05 b. 90% confidence interval

a) what are the hypothesis for this test?

b) Find the test statistic

c) Find the critical values

d) what is the conclusion of the hypothesis test

e) the 90% confidence interval is ?

Answer 1

The statistic software output for this problem is:

Two sample T summary hypothesis test: Hi : Mean of Population 1 H2 : Mean of Population 2 H1 - H2 : Difference between two means Ho: V1 - H2 = 0 HA: 41 - H2> 0 (without pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DE T-Stat P-value Pi - 2 1 2.2472205 28.180924 0.44499416 0.3299

(a)

H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ > 0

(b)

Test statistics = 0.445

(c)

df = 28

Critical value is : 1.701

(d)

Fail to reject the null hypothesis .

(e)

Two sample T summary confidence interval: Pu: Mean of Population 1 2 : Mean of Population 2 Hi-N2 : Difference between two means (without pooled variances) 90% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit Vi - 2 1 2.2472205 28.180924 -2.8219771 4.8219771

The 90% confidence interval is : (-2.822 , 4.822)