11.

a. Having obtained a random sample from a population, you wish to use a chi-squared test to decide whether the population distribution is standard normal. If you base the test on six class intervals having equal probability under H0, what should be the class intervals?

x2  a k

i1 N2i npi0

 n

b. If you wish to use a chi-squared test to test H0:

the population distribution is normal with m.5, s  .002 and the test is to be based on six equiprobable (under H0) class intervals, what should be these intervals?

c. Use the chi-squared test with the intervals of part

(b) to decide, based on the following 45 bolt diameters, whether bolt diameter is a normally distributed variable with m  .5 in., s  .002 in.

.4974 .4976 .4991 .5014 .5008 .4993

.4994 .5010 .4997 .4993 .5013 .5000

.5017 .4984 .4967 .5028 .4975 .5013

.4972 .5047 .5069 .4977 .4961 .4987

.4990 .4974 .5008 .5000 .4967 .4977

.4992 .5007 .4975 .4998 .5000 .5008

.5021 .4959 .5015 .5012 .5056 .4991

.5006 .4987 .4968 of degrees of freedom as the test in part (a)?
Explain.