# MTH 380 Lecture Notes - Lecture 8: Skilled Worker, Margarine, Statistical Parameter

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ASSIGNMENT 8, Estimation of single population parameter (mean, proportion, variance)

Part 1

Chapter 8, Large - sample estimation.

Ch.8.2, Point estimation, Ch.8.3. Interval estimation, 8.7. Choosing the sample size

Large - sample confidence interval for population mean

1. Ch.8.2, 21, p.296

A random sample of n = 75 observations from a quantitative population produced

29.7x=

and

210.8

s=

. Give the best point estimate for the population mean

µ

and

calculate the margin of error.

2. Ch.8.2, 30, p.297

3. Ch.8.2, 25, p.296 Antibiotics

You want to estimate the mean hourly yield for a process that manufactures an antibiotic.

You observe the process for 100 hourly periods chosen at random with the results

34x=

ounces per hour and standard deviation s = 3 ounces per hour.

Estimate the mean yield of the process and find 95% margin of error.

4. Ch.8.2, 35, p.297

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5.

The lifetime in hours of a 75 – watt light bulb is known to be normally distributed with

standard deviation of 25 hours. A random sample of 20 bulbs has a mean life of 1014 hours.

a. Construct a 90% CI, 95% CI and 99% CI on mean life of the bulb.

b. If we want to be 90% (95%, 99%) confident that the error in estimating mean life is no more

than 5 hours, what sample size should be used?

6.

The following observations are the ages of a random sample of eight employees at

ABC Company: 52, 68, 22, 35, 30, 56, 39,48.

It’s known that the ages of employees of ABC Company are normally distributed with a

standard deviation of 10 years.

Find 95% confidence interval for the mean age of company employees.

7.

An industrial engineer wishes to determine the average time needed for the skilled

worker to perform the certain task. She knows from previous studies that standard

deviation of probability distribution of times required to perform the certain task is

equal to 28 seconds.

a. Find a 99% confidence interval for a true mean time if a random sample of 49 workers

yielded an average time of 3 minutes and 52 seconds (232 seconds).

b. How large sample will she need if she wants to be 99% confident that the sample

mean will be within five seconds of the true population mean.

8.

An industrial engineer wishes to determine the average time needed for the skilled

worker to perform the certain task.

Find a 99% confidence interval for a true mean time if a random sample of 49 workers

yielded an average time of 3 minutes and 52 seconds (232 seconds) and a standard

deviation of 31 seconds.

9.

The yield of chemical process is being studied. The past 49 days of plant operation have resulted

in the average yield equal to 88.48 and standard deviation equal to 3 (the mean and standard

deviation are calculated from the sample data).

Find 95% confidence interval on the true mean yield.

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10. Ch.8.3, 25, p.296 (modified)

You want to estimate the mean hourly yield for a process that manufactures an antibiotic.

You observe the process for 100 hourly periods chosen at random with the results

34x=

ounces per hour and standard deviation s = 3 ounces per hour.

Estimate the mean hourly yield for a process using 95% confidence interval

11. Ch.8.3, 29, p. 306

12. Ch.8.3, 30, p.306

13. Ch.8.7, 12, p.326