Final answer:
For comparing study habits with the national average, one-sample t-tests are used. To test if the mean time spent on homework has increased, a z-test is used due to the known population standard deviation. Independent t-tests or ANOVA analyze differences between groups in various scenarios.
Step-by-step explanation:
To determine whether study habits at your college align with the national average of less than 20 hours of studying per week, you will use a one-sample t-test because the sample size is relatively small (< 30) and the population standard deviation is unknown. For the hypothesis test concerning the student academic group's claim that freshman students study at least 2.5 hours per day (150 minutes), you will need to perform a one-sample t-test to see if the mean study time of 137 minutes significantly differs from the claimed 150 minutes.
When conducting a hypothesis test to determine if students' weekly homework time has increased from the stated 2.5 hours, you will establish the null hypothesis, H0: μ = 2.5 hours, and the alternative hypothesis, H1: μ > 2.5 hours. You will use a z-test since the population standard deviation is known.
To assess whether the mean number of English courses taken by male and female college students is statistically the same, an independent t-test is appropriate due to separate samples for males and females. Similarly, to analyze if there is a difference in sports participation or class scores between groups, independent t-tests or ANOVA (Analysis of Variance) can be used depending on the number of groups and variables.
In summary, statistical tests such as hypothesis testing and t-tests provide valuable tools for comparing sample means to known values or between different groups, whereas ANOVA is useful for comparing means across multiple groups.