Final answer:
The mathematics chairperson of a prestigious university wants to test the claim that 36% of research in mathematics is published by US authors. They surveyed 278 recent articles and found that 85 have US authors. A hypothesis test using a z-test for proportions is conducted, which results in strong evidence to suggest that the percentage of research in mathematics published by US authors is no longer 36%.
Step-by-step explanation:
To test the claim that the percentage of research in mathematics published by US authors is no longer 36%, the mathematics chairperson of a prestigious university surveys a simple random sample of 278 recent articles published by reputable mathematics research journals. Out of these 278 articles, 85 have US authors. The chairperson wants to determine if this evidence supports the claim.
To analyze the evidence, we can use a hypothesis test. The null hypothesis, denoted as H0, states that the percentage of research in mathematics published by US authors is still 36%. The alternative hypothesis, denoted as Ha, states that the percentage is different from 36%. We can conduct a hypothesis test using the z-test for proportions since we have a large sample size and want to compare a sample proportion to a known population proportion.
To perform the hypothesis test, we calculate the test statistic using the formula z = (p-hat - p) / sqrt [ (p * (1-p)) / n ], where p-hat is the sample proportion, p is the hypothesized proportion (36% in this case), and n is the sample size. In this scenario, p-hat = 85/278 = 0.306 and n = 278. Substituting these values into the formula, we find that the test statistic is -4.066.
Next, we calculate the p-value associated with the test statistic. The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true. Since this is a two-tailed test, we compare the absolute value of the test statistic to the critical value (which corresponds to the desired level of significance, typically 5%). A test statistic more extreme than the critical value corresponds to a p-value less than the level of significance, indicating evidence against the null hypothesis.
Using a statistical table or calculator, we find that the p-value associated with the test statistic of -4.066 is extremely small. This means that the probability of observing a sample proportion as extreme as 0.306 (or even more extreme) under the assumption that the true population proportion is 36% is very low. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of research in mathematics published by US authors is no longer 36%.