Question

Ten different families are tested for the number of gallons of water a day they use before and after viewing a conservation video. At the 0.05 significance level, test the claim that the mean is the same before and after the viewing. Use the critical value method of hypothesis testing. What're alternative hypothesis? the critical value, test statistic and statistical conclusion? Before After 33 34 33 28 38 25 33 28 35 35 35 33 40 31 40 28 40 35 31 33

Answer 1

Sol:

Ho:$\mu before-\mu after=0$

Ha:$\mu before-\mu after \neq 0$

alpha=0.05

perform paired test in excel

Install analysis toolpak in excel

Data>Data analysis>Paired t test

T Test: Paired Two Sample for Means Before After Mean 35.8 31 Variance 11.7333333 12.44444444 Observations 10 10 Pearson Correlatio -0.1379273 Hypothesized Mea 0 df 9 t Stat 2.89392434 P(T<=t) one-tail 0.00888516 t Critical one-tail 1.83311292 P(T<=t) two-tail 0.01777032 t Critical two-tail 2.26215716

test statistic

t=2.8939  

critical t value=2.262

test statistic>critical t value

Reject Ho

Accept Ha

Conclusion:

There is no sufficient statistical evidence at 5% level of significance to conclude that the mean is the same before and after viewing.