You must show all of your work in order to receive full credit. Please round your answers to the nearest thousandths, whenever possible.

1. Construct a 95% confidence interval for the population mean if the standard deviation of the population is 12, the sample size is 70 and the sample mean is 100. (16 points)

2. Given the following data set : 35, 29, 47, 39, 50, 38, and 41. Construct a 99% confidence interval for the population mean.

A fast-food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 850 mg. A random sample of 70 breakfast sandwiches has a mean sodium content of 870 with a standard deviation of 50 mg. Use 10% significance level.

a) State the null and alternative hypotheses and identify which one represents the claim. (5 points)

b) Determine whether to reject or fail to reject the null hypothesis.

The U.S. Department of Agriculture claims that the mean consumption of coffee by a person in the United States is 35.2 gallons per year. A random sample of 150 people in the United States shows that the mean coffee consumption is 38.5 gallons per year with a standard deviation of 6.2 gallons. Use 5% level of significance.

a) State the null and alternative hypotheses and identify which represents the claim. (5 points)

b) Determine whether to reject or fail to reject the null hypothesis.

The U.S. Department of Agriculture claims that the mean consumption of coffee by a person in the United States is 35.2 gallons per year. A random sample of 150 people in the United States shows that the mean coffee consumption is 38.5 gallons per year with a standard deviation of 6.2 gallons. Use 5% level of significance.

a) State the null and alternative hypotheses and identify which represents the claim. (5 points)

b) Determine whether to reject or fail to reject the null hypothesis.

A used car dealer says that the mean price of a 2015 BMW-X5 is $68,000. You suspect this claim is incorrect and find that a random sample of 45 similar vehicles has a mean price of $62,550 and a standard deviation of $4500. Use 10% level of significance.

a) State the null and alternative hypotheses and identify which represents the claim. (5 points)

b) Determine whether to reject or fail to reject the null hypothesis. (12 points)

6. The manufacturer of Pepsi claims that its 2-liter bottles contain, on average, no more than 250 calories. A sample of 20 2-liter bottles, which were checked for calories, contains a mean of 255 calories with a standard deviation of 5.6 calories. Assume that the calorie count has a normal distribution. Does the sample information indicate that a 2-liter bottle of Pepsi contains more than 250 calories? Use 5% significance level.

a) State the null and alternative hypotheses and identify which represents the claim. (5 points)

b) Determine whether to reject or fail to reject the null hypothesis.