A Michigan study concerning preference for outdoor activities used a questionnaire with a six-point Likert-type response in which 1 designated “not important” and 6 designated “extremely important.” A random sample of n1 = 46 adults were asked about fishing as an outdoor activity. The mean response was 1 = 4.9. Another random sample of n2 = 51 adults were asked about camping as an outdoor activity. For this group, the mean response was 2 = 4.3. From previous studies, it is known that σ1 = 1.5 and σ2 = 1.2. A Likert scale usually has to do with approval of or agreement with a statement in a questionnaire. For example, respondents are asked to indicate whether they “strongly agree,” “agree,” “disagree,” or “strongly disagree” with the statement.
(a) Do these data indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity? Use a 5% level of significance.
(b) Find a 95% confidence interval for μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.
Please provide the following information for problem part (a):
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) 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 α?
(v) Interpret your conclusion in the context of the application.