Question

15. The data table represents the measure of a variable before and after a treatment. Does the sample evidence suggest that the treatment is effective in decreasing the value of the response variable? Use the a= 0.05 level of significance. Complete parts (a) through (d). Individual Before, After, y 1 40 4 2 30 3 52 5 36 50 38 33 48 47 31 (a) What type of test should be used? Choose the correct answer below. O A. A hypothesis test regarding the difference of two means using a matched-pairs design. OB. A hypothesis test regarding the difference between two population proportions from independent samples. OC. A hypothesis test regarding two population standard deviations. OD. A hypothesis test regarding the difference of two means using Welch's approximatet. (b) Determine the null and alternative hypotheses. Let Hd = x - Hy. Choose the correct answer below. O A. Ho Ho = 0; H4 Hd70 OB. Ho Hd = 0; H: Hd 0 O C. Ho Hd = 0; Hyd> OD. Ho: #0H4 Hd > 0 (c) Use technology calculate the P-value. (Round to three decimal places as needed.) (d) Draw a conclusion based on the hypothesis test. Choose the correct answer below. O A. There is sufficient evidence to reject the null hypothesis because the P-value <a O B. There is not sufficient evidence to reject the null hypothesis because the P-value > O C. There is not sufficient evidence to reject the null hypothesis because the P-value <a. D. There is sufficient evidence to reject the null hypothesis because the P-value>

Answer 1

a) A. a hypothesis test regarding the difference of two means using a matched pair design.

Calculations-

	Xi	Yi	difference (Xi - Yi)
	40	38	2
	30	33	-3
	52	48	4
	50	47	3
	36	31	5
Average	41.6	39.4	2.2
St. Dev.	9.317	7.829	3.114
n	5	5	5

- let Md = 시x-My b) To test 0. C. Hold' = 0 , Hii Hd > 0 c) Test statistic we have calculated, X, = 41.6 X2 = 39.4 5, 79.317, S2 27.829, Ō = 2.2, SD = 3.114 2-0.05. dif = 5-1. = 4 tc= 2.132 ㅎ 2.2 ta sola = 1058. 3:11415

> 0.05 t- 1.58 p-value I p. value accept Ho. O. 0942 0.0947 d) o B. There is not sufficient evidence to At reject the null bypothesis because the MP3 94 p-value ? 2.tn

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