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.

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