The p-value for the calculated t-statistic of 1.91 is approximately 0.0309.

Interpretation:

• Since the p-value (0.0309) is greater than the significance level ($\alpha = 0.01$), we do not reject the null hypothesis. This means there is insufficient evidence to conclude that the mean salary of family practitioners is significantly greater than $178,358.

If you have any questions or need further explanation, feel free to ask. Here are some related questions:

1. How do you interpret the p-value in hypothesis testing?
2. What are the implications of a small p-value versus a large p-value?
3. How does the choice of significance level affect the hypothesis test outcome?
4. What is the relationship between the p-value and the critical value?
5. How can p-values be used to determine the strength of evidence against the null hypothesis?
6. What is the difference between statistical significance and practical significance?
7. How do you adjust for multiple comparisons when calculating p-values?
8. How can you calculate p-values for different types of tests?

Tip: A smaller p-value indicates stronger evidence against the null hypothesis, while a larger p-value suggests weaker evidence.