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+ + + + + + + + + + +All exercises taken from the OpenIntro Statistics textbook, \(4^{th}\) edition, Chapter 7.
+\(H_0:\) The mean hours worked for the groups are all equal.
+\[\mu_{<~hs} = \mu_{hs} = \mu_{jc} = \mu_{ba} = \mu_{grad} \] \(H_A:\) The mean hours worked vary by education level. In other words, the means are not equal.
+Independent observations, normal(ish) distributions, and constant(ish) variance. The problem doesnât say much about the sample to help evaluate the independence of the observations, but itâs definitely less than 10% of the population and is likely a fairly good approximation of a random sample (thereby satisfying the rule of thumb). From the boxplots the distributions all look fairly normal. The standard deviations are also similar. Weâll assume that the conditions are met for the purposes of the test.
+\(H_0\): Average child care hours is the same for all attainment levels: \(\mu_{College}~=~\mu_{TechOrVoc}~=~\mu_{UMS}~=~\mu_{LMS}~=~\mu_{PS}\) \(H_A\): At least one pair of means are different.
Since \(p~>~0.05\), the results fail to reject \(H_0\). The data do not provide convincing evidence of a difference between the average number of hours spent on child care across educational attainment levels.