For Problems 1-2 the standard deviation of the population is known hence we will find the margin of error using the formula E = ZcQ n

Problem 1. A company that produces bread is concerned about the distribution of the amount of sodium in its bread. The company takes a simple random sample of 100 slices of bread and computes the sample mean to be 103 milligrams of sodium per slice. Assume that the population standard deviation is 10 milligrams. show your work

a) Construct a 95% confidence interval estimate for the mean sodium level.

b) Construct a 99% confidence interval estimate for the mean sodium level

Problem 2. Fill in the blanks with on of the following increases, decreases, or stays the same where

E = ZcQ n

a) As the sample size (n) increases, the margin of error (E) _______________________.

b) As the confidence level (C) increases, the margin of error (E) _____________________.

c) As the standard deviation ( ) increases, the margin of error (E)

For the below problem from 3 through 4, standard deviation of the population is not known we will use the formula for margin of error as E = TcS n

In exercises 3-4, you are given the sample mean and the sample standard deviation. Assume the population is normally distributed and use the T distribution define margin of error and construct a 95% confidence interval for the population mean. Interpret the results

Problem 3. In a random sample of eight people, the main commute time to work was 35.5 minutes and the standard deviation was 7.2 minutes.

Problem 4. In a random sample of 13 microwave ovens, the main repair cost was $80.00 and the standard deviation was $13.50.

Problem 5. In a recent survey of 1002 people, 701 said that they voted in a recent presidential election. Voting records show that 61% of eligible voters actually did vote.

a) Find the 95% confidence interval estimate of the proportion of people who say that they voted.

b) Are the survey results consistent with the actual voter turnout of 61%? Why or why not?

c) How would the confidence interval change if we increased the confidence level to 99%? Find the 99% confidence interval estimate to support your answer.