Question

Assume that the differences are normally distributed. Complete parts (a) through (d) below. 9 Observation X; 1 46.2 47.8 2 54.6 54.3 3 46.0 51.1 4 45.7 50.8 5 42.6 45.2 6 50.4 50.1 7 45.4 49.2 8 45.0 47.6 (a) Determine d; = x; -Y; for each pair of data. Observation 1 2 0 0 (Type integers or decimals.) 3 0 4 0 5 0 6 0 7 0 8 0 (b) Computed and sd. und to three decimal places as needed.) Sa = (Round to three decimal places as needed.) (c) Test if Ho <0 at the a=0.05 level of significance. What are the correct null and alternative hypotheses? O A. Ho:Hd <0 H:Hd > 0 O C. Ho: Ho = 0 Hii Hd <0 B. Ho: Mo <0 Hy: Ho = 0 OD. Ho: Ho>0 H:Hd <0 P-value = (Round to three decimal places as needed.)

Answer 1

Diff (T2 - T1) Sq. Dev Dev (Diff - M) Treatment 1 Treatment 2 -0.93 1.6 0.86 46.2 47.8 54.6 46 -0.3 -2.83 7.98 54.3 5.1 2.58 6.63 51.1 5.1 50.8 2.57 6.63 45.7 42.6 2.6 0.08 0.01 45.2 50.1 -0.3 -2.82 7.98 50.4 3.8 1.28 0.08 1.63 45.4 49.2 2.6 0.01 45 47.6 S: 31.72 M: 2.52

Difference Scores Calculations Mean: 2.52 µ = 0 s2 = Ssdf= 31.72/(8-1) = 4.53 s?M= S?/N = 4.53/8 = 0.57 SM= VSM= V0.57 = 0.75 T-value Calculation t= (M- H)/SM= (2.52 - 0)/0.75 = 3.36

The value of t is 3.355236. The value of p is .01216. The result is not significant at p < .01.

With 95% confidence the population mean is between 2 and 3.04, based on only 8 samples

OC. = 0 Hoi Ho' H;: Hg <O

O D. Reject the null hypothesis. There is insufficient evidence that 4, <0 at the a = 0.05 level of significance.