Question

The following two samples were collected as matched pairs. Complete parts​ (a) through​ (d) below. Pair 1 2 3 4 5 6 7 Sample 1 6 6 10 4 6 7 8 Sample 2 5 5 4 5 4 5 5 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 mud be the population mean of​ matched-pair differences for Sample 1 minus Sample 2. Choose the correct answer below. A. Upper H 0​: mudnot equals0 Upper H 1​: mudequals0 B. Upper H 0​: mudgreater than or equals0 Upper H 1​: mudless than0 C. Upper H 0​: mudless than or equals0 Upper H 1​: mudgreater than0 D. Upper H 0​: mudequals0 Upper H 1​: mudnot equals0 Your answer is correct. b. Calculate the appropriate test statistic and interpret the results of the hypothesis test using alpha equals 0.10. The test statistic is nothing. ​(Round to two decimal places as​ needed.)

Answer 1

= (1 + 1 + 6 + (-1) + 2 + 2 + 3)/7 = 2

s_d = sqrt(((1 - 2)^2 + (1 - 2)^2 + (6 - 2)^2 + (-1 - 2)^2 + (2 - 2)^2 + (2 - 2)^2 + (3 - 2)^2)/6) = 2.16

Option - D) H₀: = 0

                   H₁: 0

The test statistic t = ( - D)/(s_d/)

                             = (2 - 0)/(2.16/)

                            = 2.45

At alpha = 0.10, the critical values are t_{0.05, 6} = +/- 1.943

Since the test statistic value is greater than the positive critical value(2.45 > 1.943), so we should reject the null hypothesis.