Based on the information provided, two hypotheses could be used to test the professor's claim that students spend more than 3 hours studying for the midterm:
1) Null hypothesis (H0): The average number of hours students spend studying for the midterm exam is 3.
This matches the initial claim that the professor disputes. The null hypothesis will be rejected if there is evidence that the average is greater than 3 hours.
2) Alternative hypothesis (Ha): The average number of hours students spend studying for the midterm exam is greater than 3.
This hypothesis is consistent with the professor's claim that students study for longer than 3 hours on average. For the alternative hypothesis to be supported, the results must show an average of over 3 hours.
Some additional notes on the hypotheses:
• The null hypothesis reflects the initial claim that will be tested. The alternative hypothesis provides the alternative explanation that will be accepted if the null hypothesis is rejected.
• "3" in the null hypothesis and "greater than 3" in the alternative hypothesis represent the critical values that determine whether the hypotheses are supported or rejected.
• A one-tailed test will be used since only one direction (greater than) is being tested. The alternative hypothesis provides only one side of the comparison.
• The null hypothesis proposes an equals relation while the alternative hypothesis proposes a greater than relation. They represent opposite possibilities.
• Statistical analysis of the data will determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The alternative will be accepted if the null is rejected.
• For the alternative hypothesis to be supported, the average number of hours studying would need to be statistically significantly greater than 3. Just being greater than 3 may not be enough to reject the null hypothesis.
Does this help explain the hypotheses and key points regarding testing the professor's claim? Let me know if any part of the explanation is unclear or if you have additional questions! I can also help explain statistical hypothesis testing in more detail if needed.
The goals are:
1) Identify the null and alternative hypotheses consistent with what is being tested
2) Ensure they reflect opposite possibilities (average=3 vs. average>3 hours)
3) Determine the critical values that will indicate whether a hypothesis is supported or rejected
4) Explain how the statistical analysis will allow us to decide between the hypotheses
Please let me know if you have any other questions! I'm happy to help further explain any part of the concepts or steps.