Week 8 – Hypothesis Tests for Slope Coefficients & Conditions for Inference
1 Textbook Reading
Required Reading: Hypothesis Test for Slope & Inference Conditions
2 Concept Quiz – Due Monday by the start of class
1. Match each procedure to the question it addresses.
confidence intervals
hypothesis tests
- What are plausible values for the population parameter?
- What are plausible values for the sample statistic?
- Is the population parameter different from 0?
- Is the value of the parameter different from a specified quantity?
2. Which of the following are always true for hypothesis statements?
- They are about sample statistics.
- They are about relationships between variables.
- They are about population parameters.
- They are about differences in groups.
3. To simulate what could have happened if the [null hypothesis was true / alternative hypothesis was true], we [separate the (x, y) pairs / keep the (x, y) pairs together] and [resample with replacement / randomly reassign a new y to each x].
4. Which of the following are true about a null distribution? (select all that apply)
- It is a distribution of statistics.
- The values on the distribution represent what might have happened if the null hypothesis was true.
- The values on the distribution represent what might have happened if the alternative hypothesis was true.
- It is a distribution of sample observations.
5. Name one similarity between a permutation distribution and a bootstrap distribution.
6. Name one difference between a permutation distribution and a bootstrap distribution.
7. For linear regression, the null distribution is always centered at ____.
8. Which of the following are true about a p-value? (select all that apply)
- It is calculated assuming the null hypothesis is true.
- It is the probability the null hypothesis is true.
- It quantifies how “surprising” our data are.
- It compares the observed statistic to a distribution of values that could have happened if the null was true.
- It is calculated assuming the alternative hypothesis is true.
- It is a probability.
9. Which of the following is true about a small p-value?
- The sample statistic is unlikely to have happened by chance.
- The sample size was large.
- The sample statistic is unlikely to have happened if the null hypothesis was true.
- The sample statistic was large.
10. If you obtain a large p-value, what can you conclude about your hypotheses?
- We cannot say the alternative hypothesis is false.
- We cannot say the null hypothesis is false.
- The null hypothesis is true.
- The alternative hypothesis is true.
11. If the probability of a Type I error goes down, what can you say about the probability of a Type II error?
- The probability of a Type II error goes down.
- The probability of a Type II error stays the same.
- The probability of a Type II error goes up.
12. If you obtained a small p-value (e.g., 0.02), what could you say about what you would expect if you constructed a 95% confidence interval?
- It would contain the null hypothesized value.
- It would not contain the null hypothesized value.
- It would contain the sample statistic.
- It would contain the true population parameter.
13. In a regression table, what is the “statistic” value associated with the slope?
- a bootstrap statistic
- a z-statistic
- the sample slope statistic
- a t-statistic
14. In a regression table, how is the p-value calculated?
- Using a permutation distribution with 1000 resamples
- Using a bootstrap distribution with 1000 samples
- Using a Normal distribution
- Using a t-distribution
15. What are the required conditions for linear regression? (select all that apply)
- a random sample was taken
- equal variance of residuals
- a large sample was collected
- linear relationship between x and y
- independence of observations
- independence of variables
- normality of residuals
- normality of observations
16. In the scatterplot of stem dry mass versus stem length, what condition appears to be violated? (select all that apply)
- equal variance of residuals
- linear relationship between x and y
- independence of observations
- normality of residuals
17. Which of the following would violate the condition of independence? (select all that apply)
- collecting a non-random sample
- observations related geographically (spatially)
- observations that are related in time (temporally)
- repeated observations on the same person
- observations related biologically
18. When conducting a hypothesis test (in general), we assume the [observations / variables] are independent. When conducting a hypothesis test for a linear regression, the conditions require that the [observations / variables] are independent.
3 R Tutorial – Due Wednesday by the start of class
Required Tutorial: Randomization test for the slope
Required Tutorial: Evaluating the technical conditions in linear regression