Question

a professor has been teaching statistics for many years. their records show that the overall mean for final exam scores is 82, with a standard deviation of 10. the professor thinks this year's class of 65 students is different from the population. what would be the null and alternative hypotheses mathematically?

Answer 1

The null hypothesis (H0) would typically be that there is no significant difference between this year's class and the overall population. In mathematical notation, this would be expressed as:

H0: μ = 82

Where μ represents the population mean.

The alternative hypothesis (H1) would then be that there is a significant difference between this year's class and the overall population. In mathematical notation, this would be expressed as:

H1: μ ≠ 82

This indicates that the mean of the current year's class is not equal to the population mean. Alternatively, if you suspect that the current class may have a higher mean than the population, you could use the alternative hypothesis:

H1: μ > 82

Or if you suspect the current class may have a lower mean than the population, you could use the alternative hypothesis:

H1: μ < 82

These alternative hypotheses would depend on the specific research question or the directionality of the suspected difference.