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 = 47 adults were asked about fishing as an outdoor activity. The mean response was x1 = 4.9. Another random sample of n2 = 43 adults were asked about camping as an outdoor activity. For this group, the mean response was x2 = 5.5. From previous studies, it is known that ?1 = 1.2 and ?2 = 1.4. 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 difference ?1 − ?2. Round your answer to two decimal places.) b) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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 = 47 adults were asked about fishing as an outdoor activity. The mean response was x1 = 4.9. Another random sample of n2 = 43 adults were asked about camping as an outdoor activity. For this group, the mean response was x2 = 5.5. From previous studies, it is known that ?1 = 1.2 and ?2 = 1.4. 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 difference ?1 − ?2. Round your answer to two decimal places.)
b) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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