Final answer:
To determine if the physics lab course increases the average grade by as much as 8 points, a two-sample t-test assuming equal variances should be conducted. The null hypothesis states there is no difference in the mean grades, while the alternative hypothesis suggests the lab course results in an increased average. The t-test will reveal if there is a significant difference at the 0.05 significance level.
Step-by-step explanation:
The question is whether a lab course in physics increases the average grade by as much as 8 points. We have two sets of data: one from students who took the course with labs (an average grade of 85 with a standard deviation of 4.7) and one from students who took the course without labs (an average grade of 79 with a standard deviation of 6.1). To determine if there is a statistically significant difference between the two means, we would conduct a hypothesis test, likely a two-sample t-test assuming equal variances, given that we are asked to assume the populations are normally distributed with equal variances.
Our null hypothesis (H0) would be that there is no difference in the mean grades between the two groups, while the alternative hypothesis (H1) would be that there is a difference in the mean grades, specifically that the lab course results in an average increase of at least 8 points. The test would be two-tailed considering we are looking at the magnitude of the difference. We would calculate the test statistic, check it against the appropriate critical value for the t-distribution at a 0.05 significance level, and determine if we have enough evidence to reject the null hypothesis.
It is important to note that to specifically assess whether the laboratory course increases the average grade by as much as 8 points, a one-tailed test would be more appropriate, since we are only interested in whether the lab course results in a higher mean grade, not just any difference in general.