To test the claim, we can use a one-sample proportion test.
The null hypothesis is that the proportion of research in mathematics published by US authors is still 34%.
The alternative hypothesis is that the proportion has changed from 34%.
Let p be the proportion of articles with US authors.
Ho: p = 0.34
Ha: p ≠ 0.34
The sample proportion is given by p̂ = 55/126 = 0.4365.
The standard error for a proportion is given by sqrt(p(1-p)/n), where p is the hypothesized population proportion, and n is the sample size.
For the sample proportion p̂ = 0.4365 and n = 126, the standard error is sqrt(0.34 * 0.66 / 126) = 0.0451.
The test statistic is calculated as (p̂ - p) / SE,
= (0.4365 - 0.34) / 0.0451
= 2.15.
Step 3 of 3: Determine the p-value and conclusion:
Using a significance level of 0.05 and a two-tailed test, the critical values are +/- 1.96.
Since the test statistic of 2.15 is outside the critical values, we reject the null hypothesis.
Therefore, we have enough evidence to conclude that the percentage of research in mathematics published by US authors is no longer 34%.
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