Confidence Intervals and Hypothesis Tests: Two Samples - Florida ...
Confidence Intervals and Hypothesis Tests: Two Samples - Florida ...
Confidence Intervals and Hypothesis Tests: Two Samples - Florida ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
STATSprofessor.com<br />
Chapter 9<br />
Note: ˆp is considered the pooled estimator of the population proportion under the null’s assumption that<br />
the two groups have the same proportion.<br />
Our competing hypotheses will be: H : ( p − p ) ≤ 0 Vs. H ( p p )<br />
also)<br />
Our test statistic will be:<br />
0 1 2<br />
( pˆ ˆ<br />
entry−level − p premium ) x1 + x2<br />
z ≈ , where pˆ<br />
=<br />
⎛ 1 1 ⎞<br />
n + n<br />
pq ˆ ˆ ⎜ + ⎟<br />
n n<br />
⎝ 1 2 ⎠<br />
A<br />
: − > 0 ( = , ≠, ≥ , < are possible<br />
1 2<br />
1 2<br />
Now let us determine if we can support the claim that entry-level laptops malfunction more than<br />
premium laptops.<br />
1. Express the original claim symbolically: pentry− level > p premium<br />
2. Identify the Null <strong>and</strong> Alternative hypothesis:<br />
0<br />
( entry−level premium )<br />
( −<br />
)<br />
H : p − p ≤ 0<br />
H : p − p > 0<br />
A entry level premium<br />
3. Record the data from the problem: pentry− level = 0.047, p premium<br />
4. Calculate the test statistic:<br />
= 0.042, α = 0.01<br />
( pˆ ˆ entry−level − p premium )<br />
z ≈ =<br />
⎛ 1 1 ⎞<br />
pq ˆ ˆ ⎜ + ⎟<br />
⎝ n1 n2<br />
⎠<br />
0.005<br />
≈ 1.73<br />
⎛ 1 1 ⎞<br />
0.0448(0.9552) ⎜ + ⎟<br />
⎝11500 9300 ⎠<br />
5. Determine your rejection region: Z > 2.326<br />
6. Find the initial conclusion: Do not reject the null, Do not support the alternative<br />
7. Word your final conclusion: The sample data does not support the claim that entry-level laptops<br />
have a greater malfunction rate in the first year of owner ship than premium laptops.<br />
20
Change language