# Chi square

Chi-square goodness-of-fit test

The Ellington Dukes are a minor-league baseball team in Ellington, Georgia. As with most other minor-league teams, the Dukes rely heavily on promotions to bring fans to the ballpark. These promotions are typically aimed at fans of specific ages. The management for the Dukes has planned its current promotional schedule according to the following estimates: of fans attending Dukes games are ages to , are ages to , are ages to , are ages to , and are over .

A statistical consulting firm for the Dukes surveyed a random sample of fans attending Dukes games in order to see if these estimates are accurate. The observed frequencies in the sample of for each of the age categories are given in the top row of numbers in Table 1 below. The second row of numbers contains the frequencies expected for a random sample of fans if the Dukes' management's estimates are accurate. The bottom row of numbers in Table 1 contains the values

= (Observed frequency - Expected frequency)2

Expected frequency

for each of the age categories.

Fill in the missing values of Table 1. Then, using the level of significance, perform a test of the hypothesis that the management's estimates are accurate. 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.

AGE GROUP

0 to 12 13 to 18 19 to 35 36 to 55 over 55 Total

Observed freq 25 25 56 33 41

Expected freq ___ 18.00 ___ 45.00 36.00 180

(fo-fe)2/fe ___ 2.722 ____ 3.200 0.694

The type of test statistic (z, t, chi square, f)

The value of the test statistic: Round your ansewer to at least two decimal places ______

The p-value round your ansewer to at least two decimal places ____

Can we conclude that the management original estimates for the age distribution of fans attending Dukes games are inaccurate? Use the 0.05 level of significance (yes or no)