Question
In: Economics
One of the reasons health care costs have been rising rapidly in recent years is the...
One of the reasons health care costs have been rising rapidly in recent years is the increasing cost of malpractice insurance for physicians. Also, fear of being sued causes doctors to run more precautionary tests (possibly unnecessary) just to make sure they are not guilty of missing something. These precautionary tests also add to health care costs. The date provided below can be used to estimate the proportion of physicians over the age of 55 who have been sued at least once.
| Sample Size | 150 |
| Number of People Who Answered "Yes" | 92 |
| Number of People Who Answered "No" | 58 |
| Sample Proportion (2 decimals) | |
| Hypothesized Population Proportion | 0.50 |
| Test Statistic (2 decimals) | |
| p-value (4 decimals) | |
| Level of Significance (Alpha) | 0.05 |
| Reject Null Hypothesis? | |
| Can one conclude that the proportion of physicians over the age of 55 who have been sued at least once is greater than .50? |
a. Formulate hypotheses that can be used to see if these data can support a finding that more than half of physicians over the age of 55 have been sued at least once.
| _________ 0.50 | |
| _________ 0.50 |
b. Use the info above to compute the sample proportion of physicians over the age of 55 who have been sued at least once (to 2 decimals).
Calculate the value of the test statistic (to 2 decimals).
What is the -value (to 4 decimal places)? Do not round intermediate calculations.
c. At , what is your conclusion?
Since -value _________ , we _________(reject or fail to reject) . We conclude that we have _________(sufficient or insufficient) evidence to suggest that the proportion of physicians over the age of 55 who have been sued at least once is greater than .50.
Solutions
Expert Solution
*Answer:
Step-by-step solution
-
Step 1 of 3
a.
The aim is to state Null and Alternative hypothesis.
The Null hypothesis
The population proportion is less than or equal to half
of the physicians over the age of 
.
The alternative hypothesis
More than half of the physicians over the age of
had been sued at least once.
Comment
-
Step 2 of 3
b.
To determine sample proportion of physicians over the age of
who had been sued at least once and the p value
for the hypothesis test, do as follows:Let
denotes the number of physicians who
had been sued over the age of 
Let
be the total sample size 
The sample proportion is obtained by dividing the count of response by sample size.
The p value for the hypothesis test is
.Comment
-
Step 3 of 3
c.
The given level of significance is
and the p value 
. The value of p is lower than the level of
significance. Therefore, the researcher rejects the null
hypothesis. Hence, conclude that more than half of the
physicians over the age of 
had been sued at least once. -
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The population proportion is less than or equal to half
of the physicians over the age of 
.
More than half of the physicians over the age of
had been sued at least once.
who had been sued at least once and the p value
for the hypothesis test, do as follows:
denotes the number of physicians who
had been sued over the age of 
be the total sample size 
.
and the p value 
. The value of p is lower than the level of
significance. Therefore, the researcher rejects the null
hypothesis. Hence, conclude that more than half of the
physicians over the age of 
had been sued at least once.
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