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 specific

winter spring summer fall
observ frequency 37 36 47 50
expected freq ? 42.50 ? 42.50
f0-fe^2/fe ? 0.994 ? 1.324

Answer the following

The value of Test statistic? Round answ to at least 2 decimal points the critical value for a test with 0.10 of level of significance Round answ to at least 2 decimal points

Can we reject the hypotesis that the birthays are equally during each season of the year? use the 0.10 level of significance