The average life expectancy for residents of Hawaii is 81.48 years (travelandleisure.com, July 16, 2018). A sociologist

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The average life expectancy for residents of Hawaii is 81.48 years (travelandleisure.com, July 16, 2018). A sociologist collects data on the age at death for 50 recently deceased Michigan residents. 

a. The sociologist believes that the average life expectancy for Michigan residents is less than the average life expectancy for Hawaiian residents. Specify the competing hypotheses to test this belief.

b. Calculate the value of the test statistic and the p-value.

c. At the 1% significance level, do the data support the sociologist’s belief?

Age
76.4
76.0
76.7
75.9
79.5
83.3
77.1
82.1
66.3
73.5
79.9
78.2
82.2
81.1
81.7
71.6
77.0
71.9
84.2
68.2
80.8
77.2
73.6
78.7
82.8
82.1
75.0
87.0
75.6
73.3
82.8
79.3
75.3
87.0
85.0
73.9
77.2
74.0
80.3
82.3
79.5
81.2
81.9
80.0
84.9
76.2
74.9
80.4
82.8
73.6
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