I'd like to test the efficiency of a new bug spray. I take 30 people and...

I'd like to test the efficiency of a new bug spray. I take 30 people and randomly assign one of two bug sprays to either their right or left arm. Bug spray 1 is laboratory tested and Bug spray 2 is just vinegar. Each individual is is then THROWN INTO AN INESCAPABLE CAGE WITH MANY MOSQUITOES. (Yes, I am an evil statistician). Once 30 minutes has passed for each individual, they are released and the number of bug bites on each arm is counted. I would like to test the hypothesis that Bug spray 1 is more effective than big spray 2. The summary statistics are as follows: sample mean for bug spray 1 is 12 bites sample standard deviation for bug spray 1 is 4 sample mean for bug spray 2 is 15 bites sample standard deviation for bug spray 2 is 6 Is there evidence at the level of significance of .05 that bug spray 1 is MORE EFFECTIVE at preventing bug bites than bug spray 2 is? Explain!

Solutions

Expert Solution

H0: Null Hypothesis: ( bug spray 1 is not MORE EFFECTIVE at preventing bug bites than bug spray 2 is )

HA:Alternative Hypothesis: ( bug spray 1 is MORE EFFECTIVE at preventing bug bites than bug spray 2 is ) (Claim)

n1 = 15

1 = 12

s1 = 4

n2 = 15

2 = 15

s2 = 6

Pooled Standard Deviation is given by:

Test Statistic is given by:

= 0.05

df = 15 + 15 - 2 =28

From Table, critical value of t = - 1.701

Since calculated value of t = - 1.611 is greater than critical value of t =- 1.701, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that bug spray 1 is MORE EFFECTIVE at preventing bug bites than bug spray 2 is.

orchestra answered 1 year ago

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