1. A population distribution is known to have standard deviation 20. Determine thep-value of a test of the hypothesis that the population mean is equal to 50, if the

average of a sample of 64 observations is(a) 52.5; (b) 55.0; (c) 57.5.

2. In a certain chemical process, it is very important that a particular solution thatis to be used as a reactant have a pH of exactly 8.20. A method for determining

pH that is available for solutions of this type is known to give measurements thatare normally distributed with a mean equal to the actual pH and with a standard

deviation of .02. Suppose 10 independent measurements yielded the followingpH values:

8.18 8.17

8.16 8.15

8.17 8.21

8.22 8.16

8.19 8.18

(a) What conclusion can be drawn at the = .10 level of significance?

(b) What about at the = .05 level of significance?

3.It is known that the average height of a man residing in the United States is 5 feet10 inches and the standard deviation is 3 inches. To test the hypothesis that menin your city are average, a sample of 20 men have been chosen. The heights ofthe men in the sample follow:

Man Height in Inches Man

1 72 70.4 11

2 68.1 76 12

3 69.2 72.5 13

4 72.8 74 14

5 71.2 71.8 15

6 72.2 69.6 16

7 70.8 75.6 17

8 74 70.6 18

9 66 76.2 19

10 70.3 77 20

What do you conclude? Explain what assumptions you are making.