Homework: Homework 5 Save HW Score: 34.25%, 3.43 of 10 pts = Question Help * Sco

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Homework: Homework 5 Save HW Score: 34.25%, 3.43 of 10 pts = Question Help * Score: 0 of 1 pt 8 of 10 (5 complete) v 10.3.23-T The following two samples were collected as matched pairs. Complete parts (a) through (d) below. Pair 1 2 3 4 5 6 7 = Sample 6 7 10 3 5 6 8 Sample 4 4 4 4 3 4 3 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. OA. Ho: Hd = 0 OB. Ho: Faso Hy: +0 H1: >0 loc. Ho: d 20 OD. Ho: Ha *0 H: Hd

Explanation / Answer

(A) Hypothesis are

d = 0

d 0

Option 1 is correct.

(B) Here we will use paired t - test for two dependent means.

Here first we will calculate the difference table and then test statistic

The average difference dbar= 2.7143

The standard deviation of difference sd = 2.2887

Standard error ot the mean difference se0= sd / n = 2.2887/  7 = 0.865

Test statistic

t = dbar/se0= 2.7143/ 0.865 = 3.138

p - value = Pr(t > 3.138 ; dF = 7-1 = 6 and alpha = 0.05) = 0.02

Critical value = t6,0.05 = 2.4469

we reject the null hypothesis and say that there is significant difference between both samples.

(D) Here the assumptions are

(i) Samples are dependent [plausible Option b and option D]

(ii) Distribution of the matched pair difference between the measurements for the population is approximately normal if the number of marched pairs is less than 30. [Only option D]

so Option D is correct here only.

Sample 1 Sample 2 Difference (d) 6 4 2 7 4 3 10 4 6 3 4 -1 5 3 2 6 4 2 8 3 5 Sum 19 average 2.7143 Std. Dev. 2.2887

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