Investigators studying exercise habits in different regions of
the country surveyed a simple random sample of 421 California
adults, age 25 - 35, and an independent simple random sample of 377
Massachusetts adults, age 25 - 35.
Among other observations, the investigators noted that
(i) In the CA sample, the average number of hours/week of
exercise was 7.4, with a standard deviation of 3.3;
(ii) In the MA sample, the average number of hours/week of
exercise was 6.7, with a standard deviation of 3.5.
Based on this data, the investigators concluded that CA adults
(in this age group) exercise more than MA adults (in this age
group).
Use an appropriate test of significance to test the
investigators' claim, at the 5% significance level.
(a) State the formal hypotheses in terms of appropriate
population parameters.
(b) Find the test statistic and the p-value and explain how
you found them (i.e., where the EV and SE come from, what
distribution the test statistic follows, etc.)
(c) Summarize your conclusions in terms of the investigators'
claim.