Question

The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) μμ and standard deviation σ=0.1σ=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 10 cigarettes of this brand. The sample yields an average of 1.6 mg of nicotine. Conduct a test using a significance level of α=0.01α=0.01.

(a) The test statistic

(b) The critical value, z* =

Answer 1

Solution :

This is the right tailed test,  

The null and alternative hypothesis is ,

H0 :   = 1.5 mg

Ha : > 1.5 mg

a) Test statistic = z =

= ( - ) / / n

= (1.6 - 1.5) / 0.1 / 10

Test statistic = z = 3.16

α=0.01

P(Z > z) = 0.01

= 1 - P(Z < z) = 0.01  

= P(Z < z) = 1 - 0.01

= P(Z < z ) = 0.99

= P(Z < 2.33 ) = 0.99

z* > 2.33