Question

A 1980 study was conducted whose purpose was to compare the indoor air quality in offices
where smoking was permitted with that in offices where smoking was not permitted. Measurements were made
of carbon monoxide (CO) at 1:20 p.m. in 36 work areas where smoking was permitted and 36 work areas where
smoking was not permitted. In the sample where smoking was permitted, the mean CO = 11.6 parts per million
(ppm) and the standard deviation CO = 7.3 ppm. In the sample where smoking was not permitted, the mean CO
= 6.9 ppm and the standard deviation CO = 2.7 ppm. Test for whether or not the mean CO is significantly (α =
0.05) different in the two types of working environments.
(a) What is the null hypothesis for this problem? What is the alternative hypothesis?
(b) For this problem, would you perform a one- or two-tailed test? Explain how you reached that decision.
(c) Determine which procedure (you have learned five situations) is the appropriate statistical test to use, with
a clear explanation for your choice.
(d) Using your calculator, test the null hypothesis and present your results. Show all your work.
(e) Using statistical language (“statistic-ese”), state your conclusion and your reasoning for reaching this
conclusion. Then restate your conclusion, this time in English instead of “statistic-ese,” without including
statistical symbols or the term hypothesis. (What is the answer to the researcher’s question?)
(f) State, based on your conclusion, whether you may have committed a Type I error or a Type II error, and
what that means.

Answer 1

Assuming the mean and standard deviation of two regions being

b)We have to perform a two tailed test. This is because we are checking if the means are equal or not. A one tail test would be conducted if we were to check if one mean is greater than other.

c)We have to use a pooled estimation and check if the t statistic is greater than the significance level statistic.

d)

P(t>3.62)=0.000737

t(0.05.45dof)=2.04

Hence as t*>2.04, we reject the null hypothesis.

e)At 5% confidence level, we reject the null hypothesis to say that the mean CO is different between the two regions.

f)There is a possibility of commiting a type 1 error in the current scenario.

P(Type1)=P(Rejecting Null when Null is true)=0.000737->There is a very low probability that we would incorrectly reject null hypothesis