Question

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 x₁ = 4.9. Another random sample of n₂ = 53 adults were asked about camping as an outdoor activity. For this group, the mean response was x₂ = 4.3. From previous studies, it is known that σ₁ = 1.3 and σ₂ = 1.4. 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.

What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ₁ − μ₂. Round your answer to two decimal places.)


(iii) Find (or estimate) the P-value. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for

μ₁ − μ₂.

(Round your answers to two decimal places.)

lower limit
upper limit

Answer 1

The statistical software output for this problem is :

Test statistics = 2.21

P-value = 0.0271

Lower limit = 0.07

Upper limit = 1.13