USA Today reported that the state with the longest mean life span is Hawaii, where the population mean life span is 77 years. A random sample of 20 obituary notices in the Honoululu Advertiser gave the following information about the life span in years of Honolulu residents.
We are testing to see if the information indicates that the mean life span for Honolulu residents is less than 77.
Ho: Mu = 77
H1: Mu < 77
population standard deviation is not known, we use t test with 19 df
and we are testing at alpha = .05. So the critical value t for a left
-tailed test is -1.729 (value obtain on any critical value chart for t
The results do not have any real limitations since the sample is simple random, no bias involved in sampling.
test statistic t = (x-bar - 77)/(standard deviation/square root(n))
x-bar = 71.4
t = (71.4 - 77)/(20.65/sqrt(20))
Since -1.213 >
-1.729, we do not reject Ho and conclude there is not sufficient
evidence to support the claim that the population mean life span for
residence in Hononlulu is less than 77 years.