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 ofn₁=40adults were asked about fishing as an outdoor activity. The mean response wasx₁=4.9. Another random sample ofn₂=42adults were asked about camping as an outdoor activity. For this group, the mean response wasx₂=4.3. From previous studies, it is known that₁=1.3and₂=1.2. Does this indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity? Use a 5% level of significance.

Note: 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) What is the value of the sample test statistic? (Test the difference₁₂. Round your answer to two decimal places.)

b) Find (or estimate) theP-value. (Round your answer to four decimal places.)