Question

The following two samples were collected as matched pairs. Complete parts (a) through (d) below Pair Sample 1 6 Sample 2 45 553 3 3 6 10 4 a. State the null and alternative hypotheses to test if a difference in means exists between the populations represented by Samples 1 and 2. Let ud be the population mean of matched-pair differences for Sample 1 minus Sample 2. Choose the correct answer below

a. Calculate the appropriate test statistic and interpret the results of the hypothesis test using alpha equals 0.10

.Find the critical values (two decimal places)

Interpret the results of the hypothesis test using alpha equals 0.05.

b. Identify the p?-value and interpret the result.

c. What assumptions need to be made in order to perform this? procedure?

Answer 1

(a) Excel add - in (Mega Stat) Procedure: Step 1: In EXCEL, Select Add - Ins > Mega Stat > Hypothesis Tests. Step 2: Choose Paired Observations. Step 3: Choose Data Input. Step 4: In Group 1, enter the column of Sample 1. Step 5: In Group 2, enter the column of Sample 2. Step 6: Enter 0 Under Hypothesized difference. Step 7: Check t - test, enter Confidence level as 95.0. Step 8: Choose not equal in alternative. Step 9: Click OK. Excel add - in (Mega Stat) output: \r\n Hypothesis Test Paired Observations 0.000 hypothesized value 6.429 mean Sample 1 4.000 mean Sample 2 2.429 mean difference (Sample 1 - Sample 2) 2.149 std. dev. 0.812 std. error 7 n 6 df 2.99 t .0243 p - value (two - tailed) Thus the value of test statistic is 2.99. Conclusion: Use a significance level, alpha = 0.10. Here, the calculated value is 2.99, which is greater than the value of t_crit = 1.78. That is, t_cal (= 2.99) > t_crit (= 1.78). Therefore, by the rejection rule, reject the null hypothesis H_0.