Stat 200
Solutions to Inference Examples
These correspond to Examples 1 through 14, covered in Lecture 23
 Can't be solved, because the sample is not random.
 Can't be solved; this is a cluster sample, not an SRS.
 Can't be solved; observations are timedependent and so do not
constitute an SRS
 Can't be solved; the distribution is skewed, not normal.

 34.2 plus or minus 1.96(5.9)/(square root of 68)= (32.8, 35.6)
 Ho: mu=30 vs. Ha: mu>30; z = (34.230)/(5.9/square root of 68)=5.87,
so Pvalue is approximately 0; reject the null hypothesis and conclude that
mu>30. Note that 30 is far from being contained in the confidence interval
computed in part (a).

 9.8 plus or minus 1.645(1.2)/(square root of 62)= (9.55, 10.05)
 Ho: mu=10 vs. Ha: mu<10; z = (9.810)/(1.2/square root of 62)= 4.59,
so Pvalue=P(Z1.31)=.0951; in general this wouldn't be small enough to
reject the null hypothesis; we conclude that mu may equal 10. Note that
10 is contained in the confidence interval in (a), but just barely.
 Ho:mu=30 vs. Ha: mu>30; z = (38.130)/(10/square root of 22)= 3.8,
Pvalue = P(Z>3.8) = approximately 0; reject Ho and conclude mu>30.
 Ho: mu=1.5 vs. Ha: mu not equal to 1.5; z = (1.2781.5)/
(1.6/square root of 18)= .59, Pvalue = 2P(Z>.59)=2(.2776)= .5552;
can't reject Ho, so we conclude that mu may well equal 30.
 Ho: mu=40 vs. Ha: mu not equal to 40; z = (47.640)/(5/square root of 10)
=4.81, Pvalue = 2P(Z>4.81)= approximately 0; reject Ho and conclude
that mu does not equal 40.
 Ho: mu=20000 vs. Ha: mu<20000; z=(1969520000)/(1103/square root of 114)
=2.95, Pvalue = P(Z<2.95)=.0016; reject Ho and conclude mu<20000.
 Ho:mu=55 vs. Ha: mu>55; z =(5855)/(20/10)= 1.5, Pvalue = P(Z>1.5)
= .0668, can't reject Ho, so we conclude mu may be 55.
 Ho: mu=1250 vs. Ha: mu<1250
 z = 2, Pvalue = .0228; reject Ho and conclude mu<1250
 z = 3, Pvalue = .0013; now there is even more evidence to reject Ho.
 Given s, not sigma, so we can't solve this by the methods of Chapter 6;
we'll learn to solve such problems in Chapter 7.
 This problem involves categorical data; we'll learn how to test
hypotheses about proportions in Chapter 8.
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