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Chi square test for distribution of birth days

Are birthdays "even 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 180 people. The birth date of each person was recorded, and each of these dates was placed into one of the 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)squared/expected frequency

for each of the season categories.

fill in the missing values of table 1. Then, using the 0.05 level of significance, perform a test of the hypothesis that birthdays are equally likely during each season of the year. The complete table 2.

Table 1 Information about the sample
Winter Spring Summer Fall Total=180
Observed freq 30 44 58 48

Expected freq ? 45.00 ? 45.00

Using equation
above ? 0.022 ? 0.200

Table 2 Summary of the Hypothesis Test

Type of test statistic?

The value of the test statistic?

The critical value for a test at the 0.05 level of significance?

Can we reject the hypothesis that birthdays are equally likely during each session of the year? Use the 0.05 level of significance.

Solution Preview

Even distribution
Are birthdays "even distributed" thorough 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 180 people. The birthdate of each person was recorded, and each of these dates was placed into one of the four categories: winter(december 21-march20), spring (march 21-june 20), summer (june 21-september 20), and ...

Solution Summary

The solution provides step by step method for the calculation of chi square test statistic. Formula for the calculation and Interpretations of the results are also included.

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