Question

The effectiveness of a new bug repellent is tested on 16 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:

xtopbar =94, s=9

The new repellent is considered effective if it provides a percent repellency of at least 89. Using α=0.01, construct a hypothesis test with null hypothesis μ=89 and alternative hypothesis μ>89 to determine whether the mean repellency of the new bug repellent is greater than 89 by computing the following:

a) the degree of freedom=

(b) the critical t value=

(c) the test statistics=

Answer 1

Solution :

Given that,

Population mean = = 89

Sample mean = = 94

Sample standard deviation = s = 9

Sample size = n = 16

Level of significance = = 0.01

This is a right tailed test.

a)

Degrees of freedom = df = n - 1 = 15

b)

Critical value of  the significance level is α = 0.01, and the critical value for a right tailed test is

= 2.602

c)

The test statistics,

t = ( - )/ (s/)

= ( 94 - 89 ) / ( 9 /16 )

= 2.222

Since it is observed that t = 2.222 < = 2.602 it is then concluded that the null hypothesis is fail to reject.

Conclusion:

It is concluded that the null hypothesis Ho is fail to reject. Therefore, there is not enough evidence to claim that the population

mean μ is less than 89, at the 0.01 significance level.