Question

Sample 1	Sample 2
12.1	8.9
9.5	10.9
7.3	11.2
10.2	10.6
8.9	9.8
9.8	9.8
7.2	11.2
10.2	12.1

A.

Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population.

B. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

B-2. Find the p-value.

B-3. Do you reject the null hypothesis at the 1% level?

C. Do you reject the null hypothesis at the 10% level?

Answer 1

For sample 1

= 9.4, s1 = 1.6142, n1 = 8

For sample 2

= 10.5625, s2 = 1.0155, n2 = 8

A) H₀:

    H₁:

B) The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

                                 = (9.4 - 10.5625)/sqrt((1.6142)^2/8 + (1.0155)^2/8)

                                 = -1.724

B-2) DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

              = ((1.6142)^2/8 + (1.0155)^2/8)^2/(((1.6142)^2/8)^2/7 + ((1.0155)^2/8)^2/7)

              = 12

P-value = P(T < -1.724)

             = 0.0552

B-3) At 1% significance level, since the P-value is greater than the significance level(0.0552 > 0.01), so we should not reject the null hypothesis.

C) At 10% significance level, since the P-value is less than the significance level(0.0552 < 0.10), so we should reject the null hypothesis.