The Gallup-Healthways Well-Being Index (http://www.well-beingindex.com) provides an assessment ...

  

The Gallup-Healthways Well-Being Index (http://www.well-beingindex.com) provides an assessment measure of health and well-being of U.S. residents. By collecting periodic data on life evaluation, physical health, emotional health, healthy behavior, work environment, and basic access, this assessment measure is of immense value to researchers in diverse fields such as business, medical sciences, and journalism. The overall composite score, as well as a score in each of the above six categories, is calculated on a scale from 0 to 100, where 100 represents fully realized well-being. In 2009, the overall well-being index score of American residents was reported as 65.9.
Let the following table represent the overall well-being score of a random sample of 35 residents in Hawaii. The data set, labeled Hawaiians, can also be found on the text website.​

  

Well-Being

 

20

 

90

 

80

 

70

 

80

 

40

 

90

 

100

 

90

 

30

 

40

 

60

 

90

 

80

 

80

 

100

 

60

 

80

 

100

 

90

 

60

 

90

 

80

 

20

 

90

 

20

 

90

 

80

 

70

 

80

 

40

 

90

 

100

 

90

 

30

(1) Determine whether the well-being score of Hawaiians is more than the national average of 65.9 at the 5% significance level.

(2) Determine if fewer than 40% of Hawaiians report a score below 50 at the 5% significance level. Use your results to comment on the well-being of Hawaiians.