Question

1. suppose that a researcher is interested in the effect of a new college preparation course on scores for a stan - dardized critical thinking test with a population mean of $mu=20$. students receive training in the course and later receive the standardized test. the researcher wants to test the hypothesis that the course affected test scores.

a. in words, state the null and alternative hypotheses as they relate to the treatment in this example.
b. use symbols to state the null and alternative hypothesis.

Explanation:

• Part a:
• The null hypothesis (\(H_0\)) represents the status - quo or no - effect scenario. In this case, it means the college preparation course has no impact on the test scores.
• The alternative hypothesis (\(H_1\)) is what we are trying to find evidence for. Here, it means the college preparation course has an impact (either positive or negative) on the test scores.
• Part b:
• We use \(\mu\) to represent the population mean of the test scores after the treatment (taking the course). The null hypothesis assumes that the mean is equal to the original population mean (\(\mu_0 = 20\)). The alternative hypothesis assumes that the mean is not equal to the original population mean.

Answer:

Part a

• Null hypothesis (\(H_0\)): The new college preparation course has no effect on the scores of the standardized critical - thinking test.
• Alternative hypothesis (\(H_1\)): The new college preparation course has an effect on the scores of the standardized critical - thinking test.

Part b

• Null hypothesis (\(H_0\)): \(\mu=20\)
• Alternative hypothesis (\(H_1\)): \(\mu

eq20\)