1. The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

1306, 1313, 1187,1313, 1268,1316. 1275,1317, 1275

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

x = A.D.

s = yr

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit A.D.

upper limit A.D.

2.Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 42 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that = 7.90 ml/kg for the distribution of blood plasma.

(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

lower limit

upper limit

margin of error

(b) What conditions are necessary for your calculations? (Select all that apply.)

is known n is large is unknown the distribution of weights is normal the distribution of weights is uniform

(c) Interpret your results in the context of this problem.

99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.20 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

male firefighters