Question

2. After conducting a census in 1970, the family incomes in a certain city were found to have a mean of $14,200 with a standard deviation of $2600. A random sample of 75 families taken in 1975 produced x¯ = $14, 930 (in 1970 dollars, after adjusting for inflation). Assume throughout this problem that the standard deviation of family incomes is the same in 1975 as it was in 1970.

a) Identify each of the numbers $14200, $2600, and $14930 as a population parameter or a statistic. If the quantity is a population parameter, use the typical Greek letter notation to denote it.

(b) What is the standard error of the sample mean? Round your answer to the nearest cent.

(c) Is is appropriate to assume that the sample mean is normally distributed? Explain your reasoning.

(d) Conduct a hypothesis test to determine whether or not the mean family income in the city has changed from the 1970 mean. Use a significance level of α = 0.05.

(e) Calculate the p-value for the above test, rounding your answer to the nearest 0.0001.

(f) Construct a 99% confidence interval on the mean family income in 1975. Using only this confidence interval, decide what the decision of the test would be if a significance level of α = 0.01 were used (instead of the 0.05 level you used above).

Answer 1

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