Page 574 - Probability and Statistical Inference

12. Large-Sample Inference 551

we can write the variance of Now, the
common p can be estimated by the pooled estimator, namely,

Thus, we consider the test statistic

for large n , n when p = p .
2
1
2
1
Upper-Sided Alternative Hypothesis
Here we test H : p = p versus H : p > p . See, for example, the Figure
0
1
1
2
2
1
12.3.2. We can propose the following upper-sided approximate level a test:
Lower-Sided Alternative Hypothesis
Here we test H : p = p versus H : p < p . See, for example, the Figure
1
0
2
2
1
1
12.3.3. We can propose the following lower-sided approximate level a test:
Two-Sided Alternative Hypothesis
Here we test H : p = p versus H : p ≠ p . See, for example, the Figure
2
1
2
0
1
1
12.3.4. We can propose the following two-sided approximate level a test:.
In practice, a sample of size thirty or more is considered large.
Example 12.3.5 The members of a town council wished to estimate the
percentage of voters in favor of computerizing the local library’s present
cataloging system. A committee obtained a random sample of 300 voters,
of whom 175 indicated that they favored the proposed computerization. Let
p denote the proportion of voters in the town who favored the proposed
computerization. Then, = 175/300 = .58333. Since n = 300 is large, in
view of (12.3.18), an approximate 90% confidence interval for p will be