Standard Auto Repair Rates
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In order to set rates, an insurance company is trying to estimate the number of sick days that full time?
workers at an auto repair shop take per year. A previous study indicated that the standard deviation was 2.1 days.
a) How large a sample must be selected if the company wants to be 95% confident that the true mean differs from the sample mean by no more than 1 day?
b) Repeat part (a) using a 98% confidence interval. Which level of confidence requires larger sample size? explain…
please show work… i need to understand so I can answer other questions like this…
a) ANSWER: Sample Size = 17
Why???
SMALL SAMPLE, LEVEL OF CONFIDENCE, NORMAL POPULATION DISTRIBUTION
Margin of Error (half of confidence interval) 1
The margin of error is defined as the “radius” (or half the width) of a confidence interval for a particular statistic.
Level of Confidence 95
s = Sample standard deviation 2.1
‘z critical value’ from Look-up Table for 95% 1.96
significant digits 2
Margin of Error = (‘z critical value’) * s/SQRT(n)
n = Sample Size 17
b) ANSWER: Sample Size = 24
Why???
SMALL SAMPLE, LEVEL OF CONFIDENCE, NORMAL POPULATION DISTRIBUTION
Margin of Error (half of confidence interval) 1
The margin of error is defined as the “radius” (or half the width) of a confidence interval for a particular statistic.
Level of Confidence 98
s = Sample standard deviation 2.1
‘z critical value’ from Look-up Table for 98% 2.33
significant digits 2
Margin of Error = (‘z critical value’) * s/SQRT(n)
n = Sample Size 24
Magnatech Tubemaster – Orbital Welding System
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