Question
In: Statistics and Probability
. As health insurance costs and the number of disabled employees increase, more companies are firing...
. As health insurance costs and the number of disabled employees increase, more companies are firing these employees. A survey of 723 employers found that 195 dismiss employees as soon as they go on long-term disability.
- Construct a 95% confidence interval for the proportion of employers who dismiss employees as soon as they go on long-term disability.
- Construct a 99% confidence interval for the proportion of employers who dismiss employees as soon as they go on long-term disability.
- Which interval is wider? Explain why this is true.
Solutions
Expert Solution
a) 
= 195/723 = 0.2697
At 95% confidence interval the critical value is z* = 1.96
The 95% confidence interval for population proportion is
+/- z* * sqrt((1
-
)/n)
= 0.2697 +/- 1.96 * sqrt(0.2697 * (1 - 0.2697)/723)
= 0.2697 +/- 0.0324
= 0.2373, 0.3021
b) At 99% confidence interval the critical value is z* = 2.58
The 95% confidence interval for population proportion is
+/- z* * sqrt((1
-
)/n)
= 0.2697 +/- 2.58 * sqrt(0.2697 * (1 - 0.2697)/723)
= 0.2697 +/- 0.0426
= 0.2271, 0.3123
c) The 99% confidence interval is wider. Because if the confidence level increases, the margin of error also increases, so that the confidence interval becomes wider.
orchestra answered 2 years agoRelated Solutions
When private companies offer health insurance to their employees the insurance carrier they contract with requires...
When private companies offer health insurance to their employees
the insurance carrier they contract with requires that all
employees be obligated to participate and pay premiums whether they
wish to or not. What problem is the health insurance company trying
to avoid? How does this policy mitigate this problem?
A. Let x be the average number of employees in a group health insurance plan, and...
A. Let x be the average number of employees in a group
health insurance plan, and let y be the average
administrative cost as a percentage of claims.
x
3
7
15
33
70
y
40
35
30
27
17
Make a scatter diagram of the data and visualize the line you
think best fits the data.Use a calculator to verify that
Σx = 128, Σx2 = 6272, Σy =
149, Σy2 = 4743, and Σxy = 2896.
Compute r....
An increase in the number of people in the United States with health insurance would likely...
An increase in the number of people in the United States with
health insurance would likely cause: A. the cost of health care
services to increase as the incentive for health care providers to
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services to decrease as the incentive for health care providers to
minimize costs becomes less important. C. the cost of health care
services to decrease as the incentive for health care providers to
minimize costs...
Let x be the average number of employees in a group health insurance plan, and let...
Let x be the average number of employees in a group
health insurance plan, and let y be the average
administrative cost as a percentage of claims.
x
3
7
15
32
72
y
40
35
30
27
17
(a) Make a scatter diagram of the data and visualize the line
you think best fits the data.
Submission Data
(b) Would you say the correlation is low, moderate, or strong?
positive or negative?
moderate and negative strong and
negative low...
Let x be the average number of employees in a group health insurance plan, and let...
Let x be the average number of employees in a group
health insurance plan, and let y be the average
administrative cost as a percentage of claims.
x
3
7
15
38
70
y
40
35
30
26
16
(a) Make a scatter diagram of the data and visualize the line
you think best fits the data.
(b) Would you say the correlation is low, moderate, or strong?
positive or negative?
low and positive
moderate and positive
moderate and negative...
Let x be the average number of employees in a group health insurance plan, and let...
Let x be the average number of employees in a group
health insurance plan, and let y be the average
administrative cost as a percentage of claims.
x
3
7
15
30
73
y
40
35
30
27
20
(c) Use a calculator to verify that Σx = 128,
Σx2 = 6512, Σy = 152,
Σy2 = 4854, and Σxy = 3085. Compute
r. (Round your answer to three decimal places.)
r = ???
Let x be the average number of employees in a group health insurance plan, and let...
Let x be the average number of employees in a group
health insurance plan, and let y be the average
administrative cost as a percentage of claims.
x
3
7
15
40
71
y
40
35
30
28
19
(c) Use a calculator to verify that Σx = 136,
Σx2 = 6924, Σy = 152,
Σy2 = 4870, and Σxy = 3284. Compute
r. (Round your answer to three decimal places.)
r =
Let x be the average number of employees in a group health insurance plan, and let...
Let x be the average number of employees in a group
health insurance plan, and let y be the average
administrative cost as a percentage of claims.
x
3
7
15
31
75
y
40
35
30
26
17
(a) Make a scatter diagram of the data and visualize the line
you think best fits the data.
(b) Would you say the correlation is low, moderate, or strong?
positive or negative?
low and positive strong and negative
strong and positive...
Let x be the average number of employees in a group health insurance plan, and let...
Let x be the average number of employees in a group
health insurance plan, and let y be the average
administrative cost as a percentage of claims.
x
3
7
15
38
71
y
40
35
30
26
17
(b) Would you say the correlation is low, moderate, or strong?
positive or negative?
strong and negative
low and positive
moderate and negative
low and negative
strong and positive
moderate and positive
(c) Use a calculator to verify that Σx =...
Let x be the average number of employees in a group health insurance plan, and let...
Let x be the average number of employees in a group health
insurance plan, and let y be the average administrative cost as a
percentage of claims.
x
3
7
15
37
70
y
40
35
30
26
16
(a) Make a scatter diagram of the data and visualize the line
you think best fits the data.
(b) Would you say the correlation is low, moderate, or strong?
positive or negative?
moderate and negative
low and positive
low and negative...
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