Question

1. suppose that a researcher is interested in the effect of a new college preparation course on scores for a standardized 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:

For part a:

• The null hypothesis (\(H_0\)) in words is that the new college preparation course has no effect on the standardized critical - thinking test scores. That is, the mean score of students who took the course is the same as the population mean.
• The alternative hypothesis (\(H_1\)) in words is that the new college preparation course has an effect on the standardized critical - thinking test scores. So, the mean score of students who took the course is different from the population mean.

For part b:

• Let \(\mu\) be the population mean of the standardized critical - thinking test scores (\(\mu = 20\)) and \(\mu_{course}\) be the mean of the test scores of students who took the course.
• The null hypothesis \(H_0:\mu_{course}=\mu\) (since \(\mu = 20\), \(H_0:\mu_{course}=20\))
• The alternative hypothesis \(H_1:\mu_{course}

eq\mu\) (or \(H_1:\mu_{course}
eq20\))

Answer:

a.

• Null hypothesis (\(H_0\)): The new college preparation course has no effect on test scores.
• Alternative hypothesis (\(H_1\)): The new college preparation course has an effect on test scores.

b.

• \(H_0:\mu_{course} = 20\)
• \(H_1:\mu_{course}

eq20\)