The test statistic can be calculated using the formula:
\[ z = \frac{(p̂ - p_0)}{\sqrt{\frac{p_0(1-p_0)}{n}}} \]
where:
- \( p̂ \) is the sample proportion (55/126=0.4365),
- \( p_0 \) is the hypothesized population proportion (0.34),
- \( n \) is the sample size (126).
Plugging in the values, we get:
\[ z = \frac{(0.4365 - 0.34)}{\sqrt{\frac{0.34 * 0.66}{126}}} \]
\[ z = \frac{0.0965}{\sqrt{0.2244/126}} \]
\[ z = \frac{0.0965}{\sqrt{0.0017828571}} \]
\[ z = \frac{0.0965}{0.0422315} \]
\[ z = 2.2873 \]
Therefore, the test statistic is 2.29.
The National Academy of Science reported that 34%
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 34%
. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 126
recent articles published by reputable mathematics research journals and finds that 55
of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 34%
? Use a 0.05
level of significance.
Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.
1 answer