Question

The effectiveness of a new bug repellent is tested on 19 subjects for a 10 hour period. (Assume normally distributed population.) Based on the number and location of the bug bites, the percentage of surface area exposed protected from bites was calculated for each of the subjects. The results were as follows: ?⎯⎯⎯=95, ?=14 The new repellent is considered effective if it provides a percent repellency of at least 89. Using ?=0.05, construct a hypothesis test with null hypothesis ?=89 and alternative hypothesis ?>89 to determine whether the mean repellency of the new bug repellent is greater than 89 by computing the following:

Answer 1

null hypothesis: HO: μ		=	89
Alternate Hypothesis: Ha: μ		>	89
0.05 level with right tail test and n-1= 18 df, critical t=				1.734
Decision rule :reject Ho if test statistic t>1.734
	population mean μ=	89
	sample mean 'x̄=	95.000
	sample size   n=	19.00
	sample std deviation s=	14.000
	std error 'sx=s/√n=	3.212
	test stat t ='(x-μ)*√n/sx=	1.868
	p value      =	0.0391

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that the mean repellency of the new bug repellent is greater than 89