Question

You are conducting an experiment to see

if a test anxiety workshop significantly reduces test anxiety in
college freshman. A standard assessment of test anxiety is known to
produce a μ = 20 with a standard deviation of 9. We drawn a sample
of 81 college freshman who had taken the workshop this semester
that resulted in a mean of 18 and standard deviation of 10. Did the
workshop help reduce the anxiety?

Answer 1

To determine if the test anxiety workshop was effective, we use a z-test with the provided sample and population data. The null hypothesis represents no effect, while the alternative hypothesis suggests a reduction in anxiety. After calculating the z-value and corresponding p-value, we compare it to the significance level to draw a conclusion.

Step-by-step explanation:

To determine if a test anxiety workshop significantly reduced test anxiety among college freshmen, we analyze the given data using statistical hypothesis testing. Given a population mean (μ) of 20 and a known population standard deviation (σ) of 9, a sample of 81 college freshmen who have taken the workshop has a mean (μ) of 18 and a sample standard deviation (s) of 10. Since we have a large sample size (n=81), we can use the z-test for this hypothesis testing.

The null hypothesis (H0) is that the workshop has no effect, meaning the sample mean will be equal to the population mean. The alternative hypothesis (H1) is that the workshop reduces anxiety levels, meaning the sample mean will be less than the population mean.

To compute the z-value:

1. Calculate the standard error (SE) using the population standard deviation and sample size: SE = σ / √ n.
2. Compute the z-score using the formula: z = (μsample - μ) / SE.
3. Compare the z-score to the standard normal distribution to determine the p-value.

If the p-value is lower than the significance level (commonly α = 0.05), we reject the null hypothesis, indicating that the workshop effectively reduces test anxiety.