The mean tar content of a simple random sample of 35 unfiltered cigarettes is 21.1 mg, with a standard deviation of 3.2 mg. the mean tar content of a simple random sample of 30 filtered cigarettes is 13.2 mg with a standard deviation of 3.7 mg. at a significance level of 0.01, do the results suggest that, on average, filtered cigarettes have less tar than unfiltered cigarettes?

There is significant evidence at 0.01 significance level that filtered cigarettes have less tar than unfiltered cigarettes

Step-by-step explanation:

Let M(f) be the true mean tar content of unfiltered cigarettes

And M(u) be the true mean tar content of filtered cigarettes

Then

: M(f) = M(u)

: M(f) < M(u)

test statistic can be calculated using the formula:

where

X is the sample mean tar content of unfiltered cigarettes (21.1 mg)Y is the sample mean tar content of filtered cigarettes (13.2 mg)s(x) is the sample standard deviation of unfiltered cigarettes (3.2 mg)s(y) is the sample standard deviation of filtered cigarettes (3.7 mg)N(x) is the sample size  of unfiltered cigarettes (35)N(y) is the sample size of filtered cigarettes (30)

Then

≈9.13

p-value of the statistic ≈0 <0.01 (significance level) Thus we can reject the null hypothesis.

Yes, that is the correct formula. to solve this problem given the number of years, plug in the number of years for t and plug the whole thing into the

The answer is harsh laws are needed to control the society