Answer to Exercise 28.3: Using the 68–95–99.7 rule, the $$P$$-value is just under 0.05, and hence ‘small’ If the $$t$$-score was 0.0499, the $$P$$-value would be just larger than 0.05 and hence ‘big.’
Answer to Exercise 28.4: 1. Hypotheses are about population parameters like $$\mu$$, not sample statistics like $$\bar{x}$$. 2. Hypotheses are about parameters like $$\mu$$, not statistics like $$\bar{x}$$. The value of 36.8051 is a sample mean, but hypothesis are meant to be written before the data are collected. In any case, these hypotheses are asking to test if the sample mean is 36.8051… which we know it is. 3. 36.8051 is a sample mean, but hypothesis are meant to be written down before the data are collected. 4. 36.8051 looks like a sample mean, but hypothesis are meant to be written down before the data are collected. 5. Hypotheses are about parameters like $$\mu$$, not statistics like $$\bar{x}$$. 6. This would be fine, if the RQ was one-tailed… but it is two-tailed.