# 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.

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#### 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.