Question

According to data from the Tobacco Institute Testing Laboratory, Camel Lights King Size cigarettes contain an average of 1.4 milligrams of nicotine. An advocacy group commissions an independent test to see if the mean nicotine content is higher than the industry laboratory claims.

(a) What are H0and Ha?
(b) Suppose that the test statistic is z= 2.36. Is this result significant at the 5% level?
(c) Is the result significant at the 1% level?

Answer 1

The mean nicotine content is higher than the industry laboratory claims at the 5% level.

The mean nicotine content is higher than the industry laboratory claims at the 1% level.

Explanation:

We are given the following in the question:

Population mean, μ = 1.4 milligrams

a) First, we design the null and the alternate hypothesis

`H_(0): \mu = 1.44\text{ milligrams of nicotine}\\H_A: \mu > 1.44\text{ milligrams of nicotine}`

We use One-tailed(right) z test to perform this hypothesis.

b) Formula:

`z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }`

z = 2.36

Now,
`z_(critical) \text{ at 0.05 level of significance } = 1.64`

Since,

`z_(stat) > z_(critical)`

We reject the null hypothesis and accept the alternate hypothesis. Thus, the mean nicotine content is higher than the industry laboratory claims at the 5% level.

c) Now,
`z_(critical) \text{ at 0.01 level of significance } = 2.33`

Since,

`z_(stat) > z_(critical)`

We reject the null hypothesis and accept the alternate hypothesis. Thus, the mean nicotine content is higher than the industry laboratory claims at the 1% level.