Question

Two-Sample T Tests for B by C

C           N          Mean       SD         SE

1           25         1309.2   344.28   68.857

2           25         1060.6   138.63   27.726

Difference                      248.56   262.44   74.229

T-Tests for Mean Difference

Null Hypothesis: difference = 0

Alternative Hyp: difference ≠ 0

                                                                        Lower    Upper

Method Variances           DF          T             P       95% C.I. 95% C.I.

Pooled   Equal    48        3.35      0.0016   99.312 397.81

Satterthwaite       Unequal 31.6      3.35      0.0021   97.282 399.84

Homogeneity of Variances    DF         F              P

Folded F Test      24,24    6.17      0.0000

Cases Included 50    Missing Cases 0

1. State the appropriate hypotheses that you wish to test to conduct a two-tailed test.

(4 points)

H_o:

H_a:

2. Suppose you were asked to really conduct a one-tailed test. Use the two-tailed printout above to find the test statistic and the p-value for the one-tailed test. (4 points)

           Test Statistic: _____________         P-Value:         _____________

3. Use the confidence interval on the printout to make an inference about which of the two populations means is larger. Make sure to state your measure of reliability. (4 points)

4. State all the assumptions that are necessary for this test to be vali (5 points)

Answer 1

Solution:

(a) To State the appropriate hypotheses that you wish to test to conduct a two-tailed test:

Null hypothesis H0: µ1 = µ2

Alternative hypothesis H1: µ1 ≠ µ2

(b) Suppose you were asked to really conduct a one-tailed test. Use the two-tailed printout above to find the test statistic and the p-value for the one-tailed test:

Test Statistic : 3.35

P- value = 0.0008

(c) 95% Confidence Interval for lower bound = 99.312

  95% Confidence Interval for lower bound = 397.81

99.312 < µ1 - µ2 < 397.81

µ1 - µ2 < 0

µ1 < µ2

The population means of second brand is larger.

(d) To State all the assumptions that are necessary for this test to be valid:

• The data follows normal distribution.
• The two samples are independent.
• The data are continuous.
• Both samples are simple random samples.
• The variances of the two populations are equal.