statistics

8.41 [EX08-041] A certain adjustment to a machine will

change the length of the parts it makes but will not affect

the standard deviation. The length of the parts is normally

distributed, and the standard deviation is 0.5 mm.

After an adjustment is made, a random sample is taken to

determine the mean length of the parts now being produced.

The resulting lengths are as follows:

75.3 76.0 75.0 77.0 75.4 76.3 77.0 74.9 76.5 75.8

a. What is the parameter of interest?

b. Find the point estimate for the mean length of all

parts now being produced.

c. Find the 0.99 confidence interval for m.

8.125 [EX08-125] Nationally, the ratio of nurses to students

falls short of the recommended federal standard,

according to the USA Today article “School nurses in

short supply” (August 11, 2009). The recommendation

from the Centers for Disease Control and Prevention

(CDC) is 1 nurse per 750 students. Use the sample

below from 38 randomly selected schools in the state

of New York to test the statement “The New York

mean number of students per school nurse is significantly

higher than the CDC standard of 750.” Assume

.

1062 1070 353 675 1557 1374 459 302 1946 487 295

1047 1751 784 480 377 883 1035 332 330 989 1098

1241 778 1691 963 1645 1594 2125 338 1380 885 707

1267 1412 1037 1603 915

a. Describe the parameter of interest.

b. State the null and alternative hypothesis.

c. Calculate the value for and find the p-value

d. State your decision and conclusion using alfa=.01

9.60 [EX09-060] Use a computer or calculator to complete

the calculations and the hypothesis test for this

exercise. Delco Products, a division of General Motors,

produces commutators designed to be 18.810 mm in

overall length. (A commutator is a device used in the

electrical system of an automobile.) The following data

are the lengths of a sample of 35 commutators taken

while monitoring the manufacturing process:

18.802 18.810 18.780 18.757 18.824 18.827 18.825

18.809 18.794 18.787 18.844 18.824 18.829 18.817

18.785 18.747 18.802 18.826 18.810 18.802 18.780

18.830 18.874 18.836 18.758 18.813 18.844 18.861

18.824 18.835 18.794 18.853 18.823 18.863 18.808

Is there sufficient evidence to reject the claim that these

parts meet the design requirement “mean length is

18.810” alfa = .01 at the level of significance?