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1. The personnel department of a large corporation wants to estimate the family dental expenses of its
employees to determine the feasibility of providing a dental insurance plan. A random sample of 12
employees reveals the following family dental expenses (in dollars): 115, 370, 250, 593, 540, 225,
177, 425, 318, 182, 275, and 228.
Construct a 95% confidence interval estimate for the standard deviation of family dental expenses for
all employees of this corporation.
Upper limit =
Lower limit =
Descriptive Statistics
Sample Size, n: 12
Mean:
308.1667
Variance, s^2: 21882.7
St Dev, s:
147.928
Using statdisk software we get 95% Confidence Interval for the st dev:
104.7914 < SD < 251.1638
95% Confidence Interval for the variance:
10981.24 < VAR < 63083.26
2. The percent defective for parts produced by a manufacturing process is targeted at 4%. The process
is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14
defectives.
How many units would have to be sampled to be 95% confident that you can estimate the fraction of
defective parts within 2% (using the information from today’s sample--that is using the result that
)?
Required sample size is: 767
3. A sample of 9 production managers with over 15 years of experience has an average salary of
$71,000 and a sample standard deviation of $18,000.
Assuming that the salaries of production managers with over 15 years experience are normally
distributed, you can be 95% confident that the mean salary for all production managers with at least
15 years of experience is between what two numbers.
Upper limit =
Lower limit =
Margin of error, E = 13836.04
95% Confident the population mean is within the range:
57163.96 < mean <84836.04
4. If you are constructing a confidence interval for a single mean, the confidence interval
will___________ with an increase in the sample size.
ℎ
ℎ ℎ
5. Senior management of a consulting services firm is concerned about a growing decline in the firm’s
weekly number of billable hours. The firm expects each professional employee to spend at least 40
hours per week on work. In an effort to understand this problem better, management would like to
estimate the standard deviation of the number of hours their employees spend on work-related
activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the
management randomly selected a sample of size 51 from the available frame. The sample mean and
sample standard deviations were 48.5 and 7.5 hours, respectively.
Construct a 99% confidence interval for the standard deviation of the number of hours this firm’s
employees spend on work-related activities in a typical week.
Upper limit =
Lower limit =
ℎ
99% Confidence Interval for the st dev:
5.948265 < SD < 10.02395
6. The personnel department of a large corporation wants to estimate the family dental expenses of its
employees to determine the feasibility of providing a dental insurance plan. A random sample of 12
employees reveals the following family dental expenses (in dollars): 115, 370, 250, 593, 540, 225,
177, 425, 318, 182, 275, and 228.
Construct a 99% confidence interval estimate for the standard deviation of family dental expenses for
all employees of this corporation.
Upper limit =
Lower limit =
99% Confidence Interval for the st dev:
94.84828 < SD < 304.0824
7. Senior management of a consulting services firm is concerned about a growing decline in the firm’s
weekly number of billable hours. The firm expects each professional employee to spend at least 40
hours per week on work. In an effort to understand this problem better, management would like to
estimate the standard deviation of the number of hours their employees spend on work-related
activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the
management randomly selected a sample of size 51 from the available frame. The sample mean and
sample standard deviations were 48.5 and 7.5 hours, respectively.
Construct a 90% confidence interval for the standard deviation of the number of hours this firm’s
employees spend on work-related activities in a typical week.
Upper limit =
Lower limit =
90% Confidence Interval for the st dev:
6.454739 < SD < 8.994563
8. If a sample has 25 observations and a 99% confidence estimate for
is needed, the appropriate
value of the t-multiple required is
3 decimals
As for confidence interval we use
ℎ .
So t value is 2.797
= 24
ℎ − 1
ℎ ℎ 0.01
= 0.005
2