Residents of Hawaii have the longest life expectancies, averaging 81.3 years (travelandleisure.com, July 16, 2018). A sociologist

Question:

Residents of Hawaii have the longest life expectancies, averaging 81.3 years (travelandleisure.com, July 16, 2018). A sociologist collects data on the age at death for 50 recently deceased Michigan residents. A portion of the data is shown in the accompanying table. Assume that the population standard deviation is 5 years.

a. Construct the 95% confidence interval for the mean life expectancy of all residents of Michigan.

b. Use the 95% confidence interval to determine if the mean life expectancy of Michigan residents differs from that of Hawaiian residents.

Age at Death
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