Final answer:
The best verbal research hypothesis for this statistical analysis is that the mean estimated 'psychological health' score for professors from Valpo College is different than the actual 'psychological health' scores of 24.00. To test this hypothesis, a two-tailed test using an alpha of 0.05 is conducted.
Step-by-step explanation:
The research hypothesis (H1) for this statistical analysis would be:
d) The mean estimated 'psychological health' score for professors from Valpo College is different than the actual 'psychological health' scores of 24.00.
In this case, a two-tailed test is appropriate because we are interested in determining if the Valpo professors' scores are significantly different from the national average, either higher or lower.
The alpha level of 0.05 indicates that we are willing to accept a 5% chance of making a Type I error.
To conduct the hypothesis test, we would calculate the t-statistic using the formula:
t = (M - µ) / (SD / sqrt(N))
where M is the sample mean, µ is the population mean, SD is the standard deviation, and N is the sample size. We would then compare the calculated t-value to the critical t-values for a two-tailed test with alpha = 0.05 and degrees of freedom equal to N - 1. If the calculated t-value falls outside of the critical t-values, we reject the null hypothesis and conclude that the mean estimated 'psychological health' score for Valpo professors is significantly different from the national average.