(1 point) The effectiveness of a new bug repellent is tested on 11 subjects for

Question

(1 point) The effectiveness of a new bug repellent is tested on 11 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: x=93, s=5 The new repellent is considered effective if it provides a percent repellency of at least 90. Using =0.01, construct a hypothesis test with null hypothesis =90 and alternate hypothesis >90 to determine whether the mean repellency of the new bug repellent is greater than 90 by computing the following: (a) the degrees of freedom (b) the test statistic The final conclusion is A. We can reject the null hypothesis that =90. Our results indicate that the new bug repellent is effective. B. There is not sufficient evidence to reject the null hypothesis that =90. Our results do not provide enough evidence that the new bug repellent is effective.

Explanation / Answer

Null Hypothesis : =90

Alternate Hypothesis :  >90

X-bar = 93

SD = 5

=0.01

(a) Degree Of Freedom dF = 11-1 = 10

(b) Test Static :

t = (93-90)/(5/sqrt(10)) = 1.897

(c) P-value = 0.0435 > alpha

Therefore, conclusion is :

B. There is not sufficient evidence to reject the null hypothesis that =90. Our results do not provide enough evidence that the new bug repellent is effective.

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