Question

QUESTION 2

[25] After submitting your analysis, Chihiro noticed that the data she collected can be organized by the day of the week as can be seen in the following table.

	Vancouver	Saskatoon	Montreal	Halifax	Sums	Means
Monday	72	75	78	76	301	75.25
Tuesday	74	77	77	73	301	75.25
Wednesday	73	75	79	70	297	74.25
Thursday	75	73	76	75	299	74.75
Friday	68	67	72	65	272	68
Sums	362	367	382	359	1470
Means	72.4	73.4	76.4	71.8

∑ ?? =108,304 ?? ??

Suppose Chihiro asked you to reassess whether there are differences in the mean productivities of the four locations but this time taking into account the variability attributed to the day of week.
(1) [1] Hypotheses

(2) [8] Compute the sum of squares for groups, blocks, and error by hand. (Show your calculations.) Complete the ANOVA table below.

Source of Variation SS df MS F p-value

Day (Block)
Location (main effect)

Error

Total

P-value

(3) [2] What will you say to Chihiro based on your results? Support your answer with the appropriate statistic.

(4) [2] How has blocking changed your conclusion of the hypothesis test here compared to your conclusion in the one-way ANOVA in question 1?

(5) [2] Is there evidence of significant differences between mean productivities for different days of week? Use the appropriate F-test to justify your answer.

(6) [10] If appropriate, use a post hoc test to determine where the significance differences lie by day of the week. Assume a significance level of 0.05. Interpret your results in context.

Answer 1