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7.2 HYPOTHESIS TESTING: A SINGLE POPULATION MEAN 233
.05
0 1.645 z
Nonrejection region
Rejection region
FIGURE 7.2.5 Rejection and nonrejection regions for Example 7.2.4.
7. Calculation of test statistic.
z =
146 - 140
27> 1157 = 6
2.1548 = 2.78
8. Statistical decision. Reject since 2.78 7 1.645.
9. Conclusion. Conclude that the mean systolic blood pressure for the
sampled population is greater than 140.
10. p value. The p value for this test is 1 - .9973 = .0027, since as shown
in Appendix Table D, the area 1.00272 to the right of 2.78 is less than
.05, the area to the right of 1.645. ■
Procedures for Other Conditions If the population variance had been
known, the procedure would have been identical to the above except that the known value
of s, instead of the sample value s, would have been used in the denominator of the
computed test statistic.
Depending on what the investigators wished to conclude, either a two-sided test or
a one-sided test, with the rejection region at the lower tail of the distribution, could have
been made using the above data.
When testing a hypothesis about a single population mean, we may use Figure
6.3.3 to decide quickly whether the test statistic is z or t.
Computer Analysis To illustrate the use of computers in testing hypotheses we
consider the following example.
EXAMPLE 7.2.5
The following are the head circumferences (centimeters) at birth of 15 infants:
33.38 32.15 33.99 34.10 33.97
34.34 33.95 33.85 34.23 32.73
33.46 34.13 34.45 34.19 34.05
We wish to test H 0 : m = 34.5 against H A : m Z 34.5.
H 0