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Worksheet 17: Large Sample Confidence for a Population Mean | MATH 311, Lab Reports of Data Analysis & Statistical Methods

Material Type: Lab; Class: Statistical Concepts and Methods; Subject: Mathematics; University: Central Washington University; Term: Fall 2008;

Typology: Lab Reports

Pre 2010

Uploaded on 08/19/2009

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1. The vitamin C content of a random sample of 40 school lunches in the Bellevue school district produced a sample
mean equal to 7.6mg and the standard deviation was 3.1mg. Describe in words what µ represents in this problem.
Then, find a 90 percent confidence interval for µ. Answer: 7.6
0.806
2. In problem 1, set a 95% confidence interval for µ. Answer: 7.6
0.980 (using z=2; 7.6 0.961 with 1.96)
3. Due to variation in laboratory techniques, impurities in materials, and other unknown factors, the results of an
experiment in a chemistry lab will not always yield the same numerical answer. In an electrolysis experiment, a class
measured the amount of copper precipitated from a saturated solution of copper sulfate over a 30-minute period. The
n=45 students acquired a sample mean and standard deviation equal to .145 and .0051 moles, respectively. Set a
90% confidence interval on µ, the true unknown mean amount of copper that could be precipitated from the solution
in 30-minutes. Answer: 0.145
.00125
4. In problem 3, set a 95% confidence interval on µ. Answer: 0.145
.00152 with 2 as tabled value; with 1.96, you
get 0.145 .00149.
5. Measurements of water intake, obtained from a sample of 37 rats that had been injected with a sodium chloride
solution, produced a mean and standard deviation of 31.0 and 6.3 cubic centimeters, respectively. Set a 98%
confidence interval on the population mean µ, after first describing verbally what µ represents in this problem.
Answer 31.0 2.42.
Math 311 Fall 2008 Worksheet 17 Large Sample Confidence Intervals for a
population mean
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  1. The vitamin C content of a random sample of 40 school lunches in the Bellevue school district produced a sample mean equal to 7.6mg and the standard deviation was 3.1mg. Describe in words what μ represents in this problem.

Then, find a 90 percent confidence interval for μ. Answer: 7.6  0.

2. In problem 1, set a 95% confidence interval for μ. Answer: 7.6  0.980 (using z=2; 7.6  0.961 with 1.96)

  1. Due to variation in laboratory techniques, impurities in materials, and other unknown factors, the results of an experiment in a chemistry lab will not always yield the same numerical answer. In an electrolysis experiment, a class measured the amount of copper precipitated from a saturated solution of copper sulfate over a 30-minute period. The n=45 students acquired a sample mean and standard deviation equal to .145 and .0051 moles, respectively. Set a 90% confidence interval on μ, the true unknown mean amount of copper that could be precipitated from the solution

in 30-minutes. Answer: 0.145 .

4. In problem 3, set a 95% confidence interval on μ. Answer: 0.145  .00152 with 2 as tabled value; with 1.96, you

get 0.145.00149.

  1. Measurements of water intake, obtained from a sample of 37 rats that had been injected with a sodium chloride solution, produced a mean and standard deviation of 31.0 and 6.3 cubic centimeters, respectively. Set a 98% confidence interval on the population mean μ, after first describing verbally what μ represents in this problem. Answer 31.02.42. Math 311 Fall 2008 Worksheet 17 Large Sample Confidence Intervals for a

population mean^ 

  1. Industrial wastes and sewage dumped into our rivers and streams absorb oxygen and thereby reduce the amount of dissolved oxygen available for fish and other forms of aquatic life. One state agency requires a minimum of 5 parts per million of dissolved oxygen in order that the oxygen content be sufficient to support aquatic life. A random sample of 42 water specimens taken from a river at a specific location showed a mean and standard deviation of 4. and 2.2 parts per million, respectively. Use this information to set a 95% confidence interval on the true mean dissolved oxygen content at this site. Do you have any reason to believe that the true mean is less than 5 parts per

million? Answer: 4.7  .665 (using z=1.96). As this interval includes the value 5, there is no reason to doubt 5

as a reasonable value.

  1. A random sample of 36 Snickers candy bars showed an average calorie count of 263 with a standard deviation of 3.

Use this information to set a 98% confidence interval on^ ^. What does^ ^ represent in words? ANS: 263  1.165.

In words,^ ^ is the average calorie content of all Snickers bars of this size.

8. In problem 7, set a 90% confidence interval on^ ^. This interval should have a smaller margin of error. That

should make sense to you. If it doesn’t, figure it out.

  1. A golf ball is supposed to weigh no more than 1.62 oz. A random sample of 64 Titleist Pro VI balls gives an average weight of 1.614 oz and a standard deviation of .03 oz. Use these data to set a 99% confidence

interval on^ ^ , after first indicating what^ ^ represents in words.