1.A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the 0.10 level of significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree? 
Pine trees Spruce trees
Sample size 20 30
Mean trunk diameter (cm) 45 39
Sample variance 100 150

What is the test value for this hypothesis test?

What is the critical value?

2. A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months are given in the file ILE_and_DLH.xlsx 

Treating ILE as the response variable, use regression to fit a straight line to all 18 data points. 

Using your estimated regression output, predict the indirect labor expenses for a month in which the company has 31 direct labor hours. 

Place your answer, rounded to 1 decimal place, in the blank. Do not use any stray punctuation marks or a dollar sign. For example, 458.9 would be a legitimate entry. 
3. An investor wants to compare the risks associated with two different stocks. One way to measure the risk of a given stock is to measure the variation in the stock’s daily price changes. 

In an effort to test the claim that the variance in the daily stock price changes for stock 1 is different from the variance in the daily stock price changes for stock 2, the investor obtains a random sample of 21 daily price changes for stock 1 and 21 daily price changes for stock 2. 

The summary statistics associated with these samples are: n1 = 21, s1 = .849, n2 = 21, s2 = .529. 

If you follow Bluman’s advice and place the larger variance in the numerator, what is the test value associated with this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 3.456 would be a legitimate entry. 
4. Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 8 unacceptable assemblies. 

If you are interested in determining if there is sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies, what is the p-value associated with such a test of hypothesis? 

Place your answer, rounded to 4 decimal places, in the blank. For example, .0123 would be a legitimate entry.