Question

The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) ? μ and standard deviation ?=0.1 σ = 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 15 cigarettes of this brand. The sample yields an average of 1.4 mg of nicotine. Conduct a test using a significance level of ?=0.01 α = 0.01 . (a) The test statistic (b) The critical value, z*

Answer 1

Solution :

= 1.5

= 1.4

=0.1

n = 15

This is the right tailed test .

The null and alternative hypothesis is

H0 :   =1.5

Ha : > 1.5

Test statistic = z

= ( - ) / / n

= (1.4 -1.5) /0.1 / 15

= -3.87

p(Z >-3.87 ) = 1-P (Z < -3.87) =0.9999

P-value = 0.9999

= 0.01

The critical value = zc = 2.326

0.9999 > 0.01

Do not reject the null hypothesis .

There is insufficient evidence to suggest that