1. You have tested 10 new engines to measure the thrust (in pounds) and you obtained these results:

4061, 3637, 3215, 4581, 4373, 4138, 3701, 3244, 4520, 4298

The designers would like to know if there is evidence that mean thrust is greater than 3700 pounds. As part of determining this, respond to the following:

a. Calculate the mean and variance for this sample.

b. Is the data normally distributed? What is your conclusion about normality of the data?

c. Use a hypothesis test to determine if the mean thrust is greater than 3700. (Regardless of the answer to (b), assume that the data is normally distributed.) Use = 0.05.

d. Is there evidence that mean thrust is greater than 3700 pounds? ( "Reject" or "Fail to Reject") Explain.

2. A colleague has tested a different engine design and obtained a second sample of 10 values for engine thrust. Your colleague's sample has mean = 4073.2 pounds and standard deviation = 487.8 pounds. The mean of their sample is different from your mean and you want to determine whether this difference is statistically significant.

a. First, you need to know if the variance of thrust is different for the two engine designs that were tested. Conduct a hypothesis text to determine if the variance of the engine design you tested (in question 1) and the variance of the engine design your colleague tested are statistically different. Use = 0.05.

b. Then, based on your conclusion from (a) conduct an appropriate hypothesis test to determine if the difference in the mean thrust of the engine design you tested is statistically different from the mean thrust of the design that your colleague tested. Use = 0.01. c. Is there evidence that the thrust of the two engine designs is different? ( "Reject" or "Fail to Reject") Explain.