An obstetrician wants to determine if the distribution of births is the same for the periods January to March, April to June, July to September, and October to December. She randomly selected 10 days within each time frame and obtained the results shown in the table in the next column.

(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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January- April- July- October- September December March June 10,456 10,799 11,465 11,261 11,574 11,743 12,475 11,406 11,657 12,321 12,454 11,627 11,608 11,661 12,193 8,706 11,244 8,521 10,982 12,022 9,184 11,621 12,081 11,930 12,357 11,321 11,387 11,054 12,251 7,706 9,055 11,431 11,916 12,618 10,872 12,319 10,837 11,212 12,927 10,824 January- April- July- March June October- September December Sample size 10 10 10 10 Sum of ranks 149 207 197 197 267