Explain hypothesis testing to a friend, using the following scenario as a model. Describe the hypotheses, the sample statistic, the P-value, the meanings of type I and type II errors, and the level of significance. Discuss the significance of the results. Formulas are not required. A team of research doctors designed a new knee surgery technique utilizing much smaller incisions than the standard method. They believe recovery times are shorter when the new method is used. Under the old method, the average recovery time for full use of the knee is 4.5 months. A random sample of 38 surgeries using the new method showed the average recovery time to be 3.6 months, with sample standard deviation of 1.7 months. The P-value for the test is 0.0011. The research team states that the results are statistically significant at the 1% level of significance.
Use the following steps (i)–(v) for all hypothesis tests:
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value
(iv) Based on your answers in parts (i)–(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
(v) Your conclusion in the context of the application.