Homework – Confidence Intervals 1. A random sample of 25 is drawn from the recor

Question

Homework – Confidence Intervals

1. A random sample of 25 is drawn from the records of daily output of a large group of employees in order to estimate the population average output. The sample shows a mean of 136 units. The standard deviation of the population is known to be 24 units. (Assume the population is normally distributed.)

a. Calculate a 98% confidence interval for the average daily output of all employees.

b. Does the average output of 136 units differ significantly from the standard output of 144 units set by management? Explain briefly.

2. A simple random sample of 800 automobile owners in a large state revealed that 480 purchased cars from Japanese or European car companies. Construct a 95% confidence interval for the proportion of all automobile owners in that state who purchase cars from Japanese or European car companies.

3. There are 400 students currently studying statistics at Breakport University. The average GPA of a random sample of 50 of these students was 3.2 with a sample standard deviation of 0.2. What is a 95% confidence interval for the average GPA of all of the statistics students?

4. The average weight of a sample of 25 widgets from a recent batch is 4 pounds. The sample standard deviation is 0.2 pounds. It is reasonable to assume that the distribution of widget weights is normal.

Create a 90% confidence interval for the population average widget weight based on this sample.

5. An assembly process includes a torque wrench device that automatically tightens compressor housing bolts; the device has a known standard deviation of 3 lb-ft in the torque applied. A simple random sample of 35 nuts is selected, and the average torque to which they have been tightened is 150 lb-ft. Create a 95% confidence interval for the average torque applied during the assembly process.

6. A pharmaceutical company found that 46% of 1,000 U.S. adults surveyed knew neither their blood pressure nor their cholesterol level. Assuming the persons surveyed to be a simple random sample of the U.S. adult population, construct a 95% confidence interval for the population proportion of adults who would have given the same answer if a census had been taken instead of a survey.

7. The personnel manager of a firm with 200 employees has selected a simple random sample of 40 employees and examined their health-benefit claims over the past year. The average amount claimed was $200 with a standard deviation of $40. Construct a 95% confidence interval for the population mean.

Explanation / Answer

Ans:

1)Given that

sample mean=136

population standard deviation=24

n=25

z value for 98% Confidence interval is 2.33

98% Confidence interval for mean

=136+/-2.33*24/sqrt(25)

=136+/-11.2

=(124.8,147.2)

b)As,Confidence interval includes 144 within its limits,so it does not differs significantly from 144.

2)sample proportion=480/800=0.6

n=800

z value for 95% CI is 1.96

95% confidence interval for population proportion

=0.6+/-1.96*sqrt(0.6*0.4/800)

=0.6+/-0.034

=(0.566,0.634)

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