1.  The mean and standard deviation of the tax value of all vehicles registered in a certain state are $13,525 and $4,180 respectively. Suppose random samples of size 100 are drawn from the population of vehicles. Find the mean and standard deviation of the sample. 

2. A random sample of 12 students from a XYZ university yields mean GPA 71 with sample standard deviation 0.51. Construct a 90% confidence interval for the mean GPA of all students at the university. Assume that the numerical population of GPAs from which the sample is taken has a normal distribution. 

3. State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number μ0 and write H0: μ=μ0 and the appropriate analogous expression for Ha.) 

a. The average July temperature in a region historically has been 74.5°F. Perhaps it is higher now.

b. The average weight of a female airline passenger with luggage was 145 pounds ten years ago. The FAA believes it to be higher now.

c.  The average stipend for doctoral students in a particular discipline at a state university is $14,756. The department chairman believes that the national average is higher.

d. The average room rate in hotels in a certain region is $82.53. A travel agent believes that the average in a particular resort area is different.

e. The average farm size in a predominately rural state was 69.4 acres. The secretary of agriculture of that state asserts that it is less today.

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