Question

The National Academy of Science reported in a 1997 study that 45% 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 more than 45%. He surveys a simple random sample of 135 recent articles published by reputable mathematics research journals and finds that 68 of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is more than 45%? Use a 0.05 level of significance.

Answer 1

Perform a hypothesis test to determine if the evidence supports the claim that the percentage of US authors in mathematics research is more than 45%. Based on the sample data, there is insufficient evidence to support the claim.

Step-by-step explanation:

To determine if the evidence supports the mathematics chairperson's claim that the percentage of US authors in mathematics research is more than 45%, we need to perform a hypothesis test.

1. Step 1: Set up the hypotheses:

• Null hypothesis (H0): The percentage of US authors is 45% or less.
• Alternative hypothesis (Ha): The percentage of US authors is more than 45%.

Step 2: Identify the test statistic and determine the significance level:

• Since we are comparing proportions, we can use the z-test statistic.
• The significance level is given as 0.05.

Step 3: Compute the test statistic:

• Calculate the sample proportion of US authors: 68/135 = 0.5037
• Calculate the standard error: sqrt((0.45 * 0.55)/135) = 0.0426
• Calculate the z-test statistic: (0.5037 - 0.45)/0.0426 = 1.2488

Step 4: Determine the critical value:

• Since the alternative hypothesis is that the percentage is more than 45%, we will use the one-tail z-score critical value.
• At a significance level of 0.05, the critical value is approximately 1.645.

Step 5: Make a decision:

• If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
• In this case, the test statistic (1.2488) is less than the critical value (1.645), so we fail to reject the null hypothesis.

Step 6: State the conclusion:

• Based on the sample data, there is insufficient evidence to support the claim that the percentage of US authors in mathematics research is more than 45% at a significance level of 0.05.