An obstetrician knew that there were more live births during the week than on weekends and wanted to discover whether the distribution for number of births was the same for each of the 5 days of the week. She randomly selected eight dates for each of the 5 days of the week and obtained the data shown.

(a) State the null and alternative hypotheses.
(b) The sums of the ranks in each category are as follows:

Use this information to compute the test statistic.
(c) What is the critical value at the α = 0.05 level of significance?
(d) State your conclusion.
(e) Draw side-by-side boxplots to support your conclusion.

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Monday Tuesday Wednesday Thursday Friday 11,084 11,171 11,545 10,456 11,621 10,023 11,944 11,570 11,745 12,321 10,691 11,749 11,045 11,346 12,023 10,283 12,927 11,875 12,433 12,192 12,577 12,422 10,265 12,193 12,132 11,189 11,753 11,593 11,903 11,627 11,198 12,509 11,216 11,233 11,624 12,543 11,465 13,521 11,818 12,543 Monday Tuesday Wednesday Thursday Friday Sample size Sum of 48 226 144 194.5 2075 ranks