Question

Label the following 2-sample tests as: Proportions, Independent, and Dependent (matched-pairs). Determine the null and alternative hypothesis and whether the test is one-tailed or two-tailed. Then explain in detail the reasons behind your answers. You do not have to work the problems out.

1. The pre-test scores for 6 students were: 5, 5, 6, 7, 7, 8. The post-test scores for the same 6 students were: 7, 6, 7, 7, 9, 9. Is there a statistically significant difference between the two scores if we assume that the post-test scores were higher at the .01 level?

2. One group of 8 students took a pre-test, while another group of 7 students took a post-test. The following are the results: Pre-test: 5,6,4,3,4,6,6,7. Post-test: 6,6,8,7,9,8,8. Is there a difference between pre and post-test scores at the .01 level?

3. Two surveys were conducted asking participants whether they thought the morality of Americans was decaying or not. The percent of those who thought there was a decay in morality was 56% in survey 1, while the percent of those who thought there was a decay in morality was 59.5% in survey 2. Test the claim survey 2's percent was larger at the .05 level.

Answer 1

(1)

(i)

The 2-sample test is not Proportions, It is Means

(ii)

Dependent (matched-pairs) , because the 2 samples are not independent: the same sample is measured twice: pre-test scores and post-test scores.

(iii)

H0: Null Hypothesis: = 0 ( There is no statistically significant difference between the two scores)

HA: Alternative Hypothesis: 0 ( There is a statistically significant difference between the two scores) (Claim)

(iv) the test is two-tailed because The Alternative Hypothesis has "" sign.

(2)

(i)

The 2-sample test is not Proportions, It is Means

(ii)

Independent , because the 2 samples are independent: the sample 1: One group of 8 students t and sample 2: another group of 7 students are independent

(iii)

H0: Null Hypothesis: ( There is no statistically significant difference between the two scores)

HA: Alternative Hypothesis: ( There is a statistically significant difference between the two scores) (Claim)

(iv) the test is two-tailed because The Alternative Hypothesis has "" sign.

(3)

(i)

The 2-sample test is Proportions.

(ii)

Independent , because the 2 samples are independent: the sample 1: Parcipants of Survey 1 and sample 2: Parcipants of Survey 2 are independent

(iii)

H0: Null Hypothesis: P1 P2 ( survey 2's percent was not larger )

HA: Alternative Hypothesis: P2 < P2 (survey 2's percent was larger ) (Claim)

(iv) the test is one-tailed because The Alternative Hypothesis has "<" sign.