Question

28 11. (10 points) Ten randomly selected families are tested for the number of gallons of water a day they use before and after viewing a conservation video. The results are shown below. Before 33 33 38 33 35 35 40 40 40 31 After 34 25 28 35 33 31 28 35 33 Assume that the paired differences are normally distributed. At the 1% significance level, do the data provide sufficient evidence to conclude that the mean amount of water use after the viewing differs from the mean amount of water use before the viewing? a) State the null and alternative hypotheses symbolically. b) Check assumptions and choose an appropriate test procedure. c) Find the paired sample differences and use 1-var-stats to find the mean and the standard deviation of the paired sample differences. d) Compute the value of the test statistic e) Determine the P-value. Please show your work. ) Decide on the null hypothesis (reject H, or do not reject Ho). 8) Interpret the results of the hypothesis test.

Answer 1

The necessary calculations are done below.

Before After d=Before After (d-dbar)^2 33 34 -1 33.64 33 28 5 0.04 38 25 13 67.24 33 28 5 0.04 35 35 0 23.04 35 33 2 7.84 40 9 17.64 40 28 12 51.84 40 35 5 0.04 31 33 46.24 sum 247.6 dbar=sum(d)/10 4.8 31 -2 48 Jes1 مل 1مممل مسا Ho lld = 0 VS HUdo Where eld - mean amoundt of water before use minuse after use. b) The paired differences are normally distributed hence we we paided t- test mean: JE = 4.8 88 = (Ecd-22) War = 2476 27:5111 n- d) Test statistic ta ū Sd to 4.8 127.51|11 10 t 2-8939 les p-value - PCIEL > 2.8939) p(18-2:8939) + p1 t) 2.8939) 0.008885514 +0.008885514 0.01777103 ť p-values > D=0.01, do not reject Ho. g) Conclusion : There is insufficient exidence to conclude to that the mean amount of water use differs from the mean amount of water we before viewing after viewing