As a further examination of potential bias among collectors, we want to assess w

Question

As a further examination of potential bias among collectors, we want to assess whether there is evidence that different collectors tended to choose users of different average ages. (a) Conduct an ANOVA analysis to test whether there is significant evidence that the average ages of users observed by different collectors varied between some of the collectors. Use a significance level of alpha = 0.05 in interpreting the results of this test. (b) It has been suggested that collectors N and P selected younger users (on average) than collectors J and R. Assuming homoscedasticity (that is, that variances of age are similar for all collectors), use the relevant sample statistics and the information from your ANOVA analysis in part (b) to calculate a 95% confidence interval for (mu_j + mu_R)/2 - (mu_N + mu_P)/2. Interpret this interval.

Explanation / Answer

a) For the given ANOVA,

Null Hypothesis: There is no significant difference between the average ages of users.

Vs

Alternative Hypothesis: There is a significant difference between the average ages of users.

from the given ANOVA table,

F-cal > F-critical,

hence wew reject the null hypothesis at 0.05 level of significance.

Hence there is a significant evidence that the average ages of users observed by different collectors varied between

some of the collectors.

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