Question

Individual actions can play a large rol erall health of our planet. A resea interested in evaluating environ friendly behaviors evaluated how ofter ple recycle (per month) based on whe have an overall optimistic or an overall mistic attitude toward eco-friendly beha The results from this hypothetical stu given in the table. large role in the A researcher environmentally how often peo- d on whether they n overall pessi friendly behaviors. othetical study are Pessimistic Optimistic ooow - No (a) Test whether or not recycling behaviors differed between groups using a .05 level of significance. State the value of the test statistic and the decision to retain or reject the null hypothesis.

Answer 1

Following is the output of descriptive statistics and box plot:

Descriptive statistics Pessimistic, X1 Optimistic, X2 count 10 10 2.90 6.80 mean sample standard deviation 2.13 1.69 4.54 2.84 sample variance minimum 0 maximum 6 9 5 range ВоXPlot 0 1 2 4 5 6 7 Pessimistic, X1 ВоХPlot 2 4 5 6 7 8 9 10 Optimistic, X2

Box plots shows that both distributions are approximately symmetric and there is no outlier so we can assume that data come from normal population.

That is we can use t test for independent samples

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Here we have -2.9, 5, -2.13, п,310 х, -6.8,5, %3D1.69, п,310 Hypotheses are: 0 - H a Test is two tailed. Level of significance: a-0.05 Since we can assume that variances are equal so degree of freedom of t test will be: df 3Dn +п, -2 -18 The pooled standard deviation is: (n-1)s(n-1)s2, -1.9226 п+п, -2 Test Statistics: (-(4 ((2.9-6.8)-0)/(1.9226* sqrt((1/10)+(1/10)) t= 1 1 =-4.54 п, Critical value: 2.101 Rejection Region: If Itl >2.101, Reject HO Decision: Since test statistics lies in rejection region so we reject the null hypothesis. P-value: P-value-0.0003 Decision: Since p-value is less than level of significance so we reject the null hypothesis =TINV (0.05,18) =TDIST(4.54,18,2) Excel function for critical value: Excel function for p-value:

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Conclusion: There is evidence to conclude that recycling behaviors differed between groups.