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# Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others?

Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain in the Northwest asked just this question. Some data collected by the chain are summarized in Table 1 below.

The data were obtained from a random sample of 170 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of Table 1 are the observed frequencies in the sample for each of these season categories. The numbers in the second row of Table 1 are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The numbers in the bottom row of Table 1 are the values

= (Observed frequency - Expected frequency)2

Expected frequency

for each of the season categories.
Fill in the missing values of Table 1. Then, using the level of significance, perform a test of the hypothesis that birthdays are equally likely during each season of the year. Then complete Table 2.

Round your responses for the expected frequencies in Table 1 to at least two decimal places. Round your responses in Table 1 to at least three decimal places. Round your responses in Table 2 as specified

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