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...

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
n
₁
= 45 adults were asked about fishing as an outdoor activity. The mean response was x₁
= 4.9. Another random sample of
n
₂
= 55 adults were asked about camping as an outdoor activity. For this group, the mean response was x₂
= 4.0. From previous studies, it is known that σ₁
= 1.5 and σ₂
= 2.0. 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.