# Stat 200 Solutions to Inference Examples

These correspond to Examples 1 through 14, covered in Lecture 23

1. Can't be solved, because the sample is not random.
2. Can't be solved; this is a cluster sample, not an SRS.
3. Can't be solved; observations are time-dependent and so do not constitute an SRS
4. Can't be solved; the distribution is skewed, not normal.
5.
1. 34.2 plus or minus 1.96(5.9)/(square root of 68)= (32.8, 35.6)
2. Ho: mu=30 vs. Ha: mu>30; z = (34.2-30)/(5.9/square root of 68)=5.87, so P-value 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).
6.
1. 9.8 plus or minus 1.645(1.2)/(square root of 62)= (9.55, 10.05)
2. Ho: mu=10 vs. Ha: mu<10; z = (9.8-10)/(1.2/square root of 62)= -4.59, so P-value=P(Z-1.31)=.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.
7. Ho:mu=30 vs. Ha: mu>30; z = (38.1-30)/(10/square root of 22)= 3.8, P-value = P(Z>3.8) = approximately 0; reject Ho and conclude mu>30.
8. Ho: mu=1.5 vs. Ha: mu not equal to 1.5; z = (1.278-1.5)/ (1.6/square root of 18)= -.59, P-value = 2P(Z>|-.59|)=2(.2776)= .5552; can't reject Ho, so we conclude that mu may well equal 30.
9. Ho: mu=40 vs. Ha: mu not equal to 40; z = (47.6-40)/(5/square root of 10) =4.81, P-value = 2P(Z>|4.81|)= approximately 0; reject Ho and conclude that mu does not equal 40.
10. Ho: mu=20000 vs. Ha: mu<20000; z=(19695-20000)/(1103/square root of 114) =-2.95, P-value = P(Z<-2.95)=.0016; reject Ho and conclude mu<20000.
11. Ho:mu=55 vs. Ha: mu>55; z =(58-55)/(20/10)= 1.5, P-value = P(Z>1.5) = .0668, can't reject Ho, so we conclude mu may be 55.
12. Ho: mu=1250 vs. Ha: mu<1250
1. z = -2, P-value = .0228; reject Ho and conclude mu<1250
2. z = -3, P-value = .0013; now there is even more evidence to reject Ho.
13. 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.
14. This problem involves categorical data; we'll learn how to test hypotheses about proportions in Chapter 8.