Question

Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed.

​(a) Test whether mu 1 μ1 greater than > mu 2 μ2 at the alpha α equals = 0.05 0.05 level of significance for the given sample data.

​(b) Construct a 95​% confidence interval about mu 1 μ1 minus − mu 2 μ2.

Population 1 Population 2

N 22    N 23

X 50.3 X 48.2

S 5.6 S 10.6

​(a) Identify the null and alternative hypotheses for this test

A. Upper H 0 H0​: mu 1 μ1 equals = mu 2 μ2 Upper H 1 H1​: mu 1 μ1 greater than > mu 2 μ2 --Your answer is correct

. B. Upper H 0 H0​: mu 1 μ1 less than < mu 2 μ2 Upper H 1 H1​: mu 1 μ1 equals = mu 2 μ2

C. Upper H 0 H0​: mu 1 μ1 greater than > mu 2 μ2 Upper H 1 H1​: mu 1 μ1 equals = mu 2 μ2

D. Upper H 0 H0​: mu 1 μ1 equals = mu 2 μ2 Upper H 1 H1​: mu 1 μ1 less than < mu 2 μ2

E. Upper H 0 H0​: mu 1 μ1 equals = mu 2 μ2 Upper H 1 H1​: mu 1 μ1 not equals ≠ mu 2 μ2

F. Upper H 0 H0​: mu 1 μ1 not equals ≠ mu 2 μ2 Upper H 1 H1​: mu 1 μ1 equals = mu 2 μ2

C) Find the test statistic for this hypothesis test. ____ ​(Round to two decimal places as​ needed.)

Answer 1

a).

The hypotheses for this test can be constructed as:

Null hypothesis:

Alternative hypothesis:

Thus, Option A) is correct.

b).

The confidence interval can be obtained using two sample t test.

Now, the degree of freedom = N₁+N₂-2 = 22 + 23 - 2 = 43

The t critical value at 0.05 level of significance with 43 degree of freedom from the t value table is 2.02.

Now, the confidence interval can be obtained as:

c). The value of the test statistic can be obtained as:

Thus, the value of the test statistic is 0.84.