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.

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 essay followed the normal distribution with a population standard deviation of 2.44 words per essay. For her 10 a.m. section of 40 students, the mean number of misspelled words was 6.05. Construct a 95% confidence interval for the mean number of misspelled words in the population of student essays.

Use Appendix B.to locate the value of t under the following conditions.

a. The sample size is 12 and the level of confidence is 95%.

b. The sample size is 20 and the level of confidence is 98%.

c. The sample size is 12and the level of confidence is 90%.

The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. Asample of 16 people reveals the mean yearly consumption to be 45 gallons with a standard deviation of 20 gallons. Assume the population distribution is normal.

a. What is the value of the population mean? What is the best estimate of this value? b. Explain why we need to use the t distribution. What assumption do you need to make?

c. For a 90% confidence interval, what is the value of t?

d. Develop the 90% confidence interval for the population mean.

e. Would it be reasonable to conclude that the population mean is 48 gallons?

A recent survey of 50 executives who were laid off during a recent recession revealed it took a mean of 26 weeks for them to find another position. The standard deviation of the sample was 2.6 weeks. Construct a 95% confidence interval for the population mean. Is it reasonable that the population mean is 28 weeks? Justify your answer.