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.
72,68,81,93,56,19,78,94,83,84,77,69,85,97,75,71,86,47,66,27
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
since 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 distribution)
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
s= 20.65
t = (71.4 - 77)/(20.65/sqrt(20))
t= -1.213
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.