To compute the test statistic, we can use the formula for a test statistic for a hypothesis test involving a single population proportion:
\[ z = \frac{(p̂ - p)}{\sqrt{\frac{p(1-p)}{n}}} \]
where
- p̂ is the sample proportion (46/208 = 0.2212),
- p is the hypothesized population proportion (0.31), and
- n is the sample size (208).
Plugging in the values, we get:
\[ z = \frac{(0.2212 - 0.31)}{\sqrt{\frac{0.31(1-0.31)}{208}}} \]
\[ z = \frac{-0.0888}{\sqrt{\frac{0.31(0.69)}{208}}} \]
\[ z = \frac{-0.0888}{\sqrt{\frac{0.2139}{208}}} \]
\[ z = \frac{-0.0888}{\sqrt{0.001027}} \]
\[ z = \frac{-0.0888}{0.03206} \]
\[ z = -2.7725 \]
Therefore, the value of the test statistic is -2.77 (rounded to two decimal places).
The National Academy of Science reported that 31%
of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 31%
. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 208
recent articles published by reputable mathematics research journals and finds that 46
of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 31%
? Use a 0.02
level of significance.
Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.
1 answer