Question

- McFarland Insurance Company knows that the average cost to process a claim for their company is currently $60. Given the economic conditions they initiated cost-cutting measures. To evaluate the effectiveness of these measures after six months, McFarland selected at random 26 claims and determined the cost to process them. The sample information is as follows:

$45 |
49 |
62 |
40 |
43 |
61 |

48 |
53 |
67 |
63 |
78 |
64 |

48 |
54 |
51 |
56 |
63 |
69 |

58 |
51 |
58 |
59 |
56 |
57 |

38 |
76 |

- (3) Calculate the mean and standard deviation of the sample data. You may use Excel for this.
- (5) Derive a 99% confidence interval for the average cost of processing a claim after the cost cutting measures were implemented.
- (5) Perform the hypothesis test to determine if the measures reduced the cost of processing the claims from the current level. Use alpha = 0.01.
- (3) Could you have drawn the conclusion you reached in part c using the information from part b? Explain why or why not. (You will need to think about this one!)
- (1) What assumption is necessary to conduct these tests?

Answer #1

An
Insurance Company reports that the mean cost to process claim is
$50. An industry comparison showed this amount to be larger than
most other insurance companies, so they instituted cost-cutting
measures. To evaluate the effect of cost-cutting measure, the
company selected a random sample of claims processed last month and
determine the cost to process these selected claims. The sample
information is reported as follows: 45, 48, 52, 58, 38, 42. At the
0.05 significance level is it reasonable...

An
Insurance Company reports that the mean cost to process claim is
$50. An industry comparison showed this amount to be larger than
most other insurance companies, so they instituted cost-cutting
measures. To evaluate the effect of cost-cutting measure, the
company selected a random sample of claims processed last month and
determine the cost to process these selected claims. The sample
information is reported as follows: 45, 48, 52, 47, 39, 42. At the
0.10 significance level is it reasonable...

An
Insurance Company reports that the mean cost to process claim is
$50. An industry comparison showed this amount to be larger than
most other insurance companies, so they instituted cost-cutting
measures. To evaluate the effect of cost-cutting measure, the
company selected a random sample of claims processed last month and
determine the cost to process these selected claims. The sample
information is reported as follows: 45, 48, 52, 47, 39, 42. At the
0.10 significance level is it reasonable...

An
Insurance Company reports that the mean cost to process claim is
$50. An industry comparison showed this amount to be larger than
most other insurance companies, so they instituted cost-cutting
measures. To evaluate the effect of cost-cutting measure, the
company selected a random sample of claims processed last month and
determine the cost to process these selected claims. The sample
information is reported as follows: 45, 48, 52, 47, 39, 42. At the
0.10 significance level is it reasonable...

An Insurance Company reports that the mean cost to process claim
is $50. An industry comparison showed this amount to be larger than
most other insurance companies, so they instituted cost-cutting
measures. To evaluate the effect of cost-cutting measure, the
company selected a random sample of claims processed last month and
determine the cost to process these selected claims. The sample
information is reported as follows: 40, 34, 52, 41, 32, 42. At the
0.01 significance level is it reasonable...

Therefore, McFarland has instituted cost-cutting measures in an
attempt to reduce
this cost
and a sample of 15 claims from the prior month were randomly
selected
to
determine if these new measures have indeed caused a reduction in
process
claim
costs.
At a 95.00%
confidence level, is it reasonable to conclude that the MEAN.P to
process
a claim is
now less than $60?
45
49
62
40
43
61
48
53
67
63
78
64
48
54
51

1. 1. McFarland Insurance Company claims department reports the
mean cost to process a claim is $60. The company wants to evaluate
an instituted cost-cutting measure. The claims department selected
a random sample of 26 claims processed last month and recorded the
cost to process each claim. The sample mean was $56.77 with a
sample standard deviation of $8.75. At the 1% significance level,
is it reasonable to conclude that the mean cost to process a claim
is different from...

The amount of time it takes for a given insurance company to
process each insurance claim is normally distributed. To better
gauge the processing time, a sample of 16 insurance claims were
collected. The sample mean of processing times was 5.4 days and the
sample standard deviation was 2.2 days. Based on this sample
a) Find the probability that the standard deviation of the
processing time of insurance claims is smaller than 3 days.
b) Find the probability that the...

The amount of time it takes for a given insurance company to
process each insurance claim is normally distributed. To better
gauge the processing time, a sample of 16 insurance claims were
collected. The sample mean of processing times was 5.4 days and the
sample standard deviation was 2.2 days. Based on this sample
a) Find the probability that the standard deviation of the
processing time of insurance claims is smaller than 3 days.
b) Find the probability that the...

2. Insurance companies want to reduce the amount of time to
approve a lifetime insurance application. The approval process
consists of underwriting, including reviewing applications,
checking health information, possible requests for additional
health information and health tests, and stages of policy
formulation and delivery. The ability to approve in a timely manner
is crucial for the benefits of this service. Following is the
processing time until it is approved (in days) of 27 random samples
of approved policies:
73 19...

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