Two sun blockers are to be compared. One blocker is rubbed on one side of a subj

Question

Two sun blockers are to be compared. One blocker is rubbed on one side of a subject's back and the other blocker is rubbed on the other side. Each subject then lies in the sun for two hours. waiting After waiting an additional hour, each side is rated according to redness. (a) Compute the difference of the two blockers for each subject. (b) Compute the mean of the difference for the two blockers. (c) According the redness data, the researcher claims that blocker 2 is more effective than blocker 1. Formulate the null and alternative hypotheses. (d) Conduct a hypothesis test at the level of significance 1% using critical value. (e) Give a full - sentence conclusion that clearly states your decision.

Explanation / Answer

Null Hypothesis : H0 :  There is no difference in the effectiveness of two blockers. d =0

Alternative Hypothesis : Ha : There is significant difference in the effectiveness of two blockers.  d > 0

where d = i1 -i2

Here i have drawn the difference table

HEre dbar = 2

sd = 1.41

For dF = 5-1 = 4 and alpha = 0.01

tcritical = 3.747

HEre test statistic

t = (dbar ) / (sd /n) = 2/ (1.41/5) = 3.17

so here t < tcriticalso we cannot reject the null hypothesis and can conclude that there is no significant differene between two blockers in their effectiveness.

Sub . NO. Blocker 1 Blocker 2 d 1 2 2 0 2 7 5 2 3 8 4 4 4 3 1 2 5 5 3 2 average 2

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