Question

For questions 1 and 2, refer to the following: The Federal Trade Commission provided measured tar contents (in mg) of randomly selected filtered and nonfiltered king-size cigarettes. A random sample of 21 filtered king-size cigarettes has a mean tar content of 13.3 mg with standard deviation 3.7 mg. A random sample of 8 nonfiltered king-size cigarettes has a mean tar content of 24.0 mg with standard deviation 1.7 mg. Assuming unequal variances between the two populations of cigarettes, you need to test the claim that the mean amount of tar in filtered king-size cigarettes is less than the mean amount of tar in nonfiltered king-size cigarettes at a

0.05 significance level.

1. What is the most appropriate statistical test?
   1. Two-sample z-test
   2. Two-sample t-test (pooled variance)
   3. Two-sample t-test (unpooled variance)
   4. Paired t test
   5. Two-way ANOVA

2. What should you use for the value of the test statistic?

a. -17.16

b. -10.70

c. -10.63

d. -7.80

e. -1.90

Answer 1

The correct option is (C), i.e., Two sample t-test(unpooled variance)

The null and alternative hypothesis is:

The formula for the two-sample t-test (unpooled variance)/Non-equal variance is:

; with df=n-1 , where we use the smaller value of n for calculating the df.

The following data is given in the question:

	Filtered (king-size cigarette)	Nonfiltered (king-size cigarette)
sample mean
sample standard deviation
sample size

Calculation for test-statistic:

                                                    

So, the test-statistic is calculated as t=-10.63

Critical Value:

Decision:

Since,

At the data does provide enough evidence to support the alternative hypothesis, i.e., . In other words we can say that, the true mean amount of tar in filtered cigarettes is less than the true mean amount of tar in Nonfiltered cigarettes