# Confidence Interval for Population Mean & Proportion

Questions

A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean.

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Dr. Patton is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per easy followed the normal distribution with a standard deviation of 2.44 words per essay. For her 10:00 am section of 40 students, the mean number of misspelled words was 6.05. Construct a 95 percent confidence interval for the mean number of misspelled words in the population of student essays.

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The American Sugar Producers Assn. wants to estimate the mean yearly sugar consumption. A sample of 16 students reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.

What is the value of the population mean? What is the best estimate value?

Explain why one would need to use the t distribution and what assumption would one make.

For a 90% confidence internal, what is the value of t?

Develop the 90% confidence interval for the population mean and would it be reasonable to conclude that the population mean is 63 pounds?

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Ms. Wilson is considering running for mayor of the town of Bear Gulch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters reveals that 300 would support her in the November election.

Estimate the value of the population proportion.

Develop a 99 percent confidence interval for the population proportion.

Interpret your findings.

#### Solution Summary

The solution provides step by step method for the calculation of confidence interval for population mean and population proportion. Formula for the calculation and Interpretations of the results are also included.