Question

According to data from the Tobacco Institute Testing Laboratory, a certain brand of cigarette contains an average of 1.4 milligrams of nicotine. An advocacy group questions this figure, and commissions an independent test to see if the the mean nicotine content is higher than the industry laboratory claims. The test involved randomly selecting ?=15n=15 cigarettes, measuring the nicotine content (in milligrams) of each cigarette. The data is given below:

       1.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.5

(a) State null and alternative hypothesis.

(b) Obtain critical value of the test.

(c) Calculate the value of test-statistic.

(d) Write your conclusion based on the data.

(e) What assumptions did you consider in the test?

PLEASE SHOW ALL WORK

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 1.4
Alternative Hypothesis, Ha: μ > 1.4

b)
Rejection Region
This is right tailed test, for α = 0.05 and df = 14
Critical value of t is 1.761.
Hence reject H0 if t > 1.761

c)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1.55 - 1.4)/(0.2416/sqrt(15))
t = 2.405

d)
Reject the null hypothesis.

There is sufficient evidence to conclude that the the the mean nicotine content is higher than the industry laboratory claims.

e)
The assumption is data is normally distributed
and data sample are taken randomly