The Ellington Dukes are a minor-league baseball team in Ellington, Georgia. Like most minor-league teams, the Dukes heavily rely on promotions to attract fans to the ballpark. These promotions aim at specific ages, with the management planning the current promotional schedule based on these estimates: 15% of fans are ages 0 to 12, 10% are ages 13 to 18, 30% are ages 19 to 35, 25% are ages 36 to 55, and 20% are over 55.A statistical firm surveyed 150 fans to test the accuracy of these estimates. Observed frequency data per age category is presented, along with the expected frequency figures based on the 150 fans, if estimates are correct. The formula for calculating the goodness of fit is provided:\[\frac{(O - E)^2}{E} = \text{(Observed frequency - Expected frequency)}^2 / \text{Expected frequency}\]### Part 1Complete the table by filling in missing values and calculating expected frequencies to two or more decimal places. Round your responses for \((O_i - E_i)^2 / E_i\) to three or more decimal places.#### Table:- **Age Group:** - 0 to 12 - 13 to 18 - 19 to 35 - 36 to 55 - Over 55 - **Observed Frequency, \(O\):** 24, 26, 51, 27, 22- **Expected Frequency, \(E\):** 22.50 for \(0-12\); 15.00 for \(13-18\); 45.00 for \(19-35\); 37.50 for \(36-55\); 30 - **\( (O - E)^2 / E \):** - \(0-12\): 0.100 - \(13-18\): 8.067 - \(19-35\): 0.800 - \(36-55\): 2.940 - \(Over 55\): Not provided ### Part 2Summarize the test of the hypothesis at a 0.05 level of significance:(a) **Test Statistic Type:** Choose the test statistic.(b) **Value

Solution: The given table of data is

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: 15% of fans attending Dukes games are ages 0 to 12, 10% are ages 13 to 18, 30% are ages 19 to 35, 25% are ages 36 to 55, and 20% are over 55. A statistical consulting firm for the Dukes surveyed a random sample of 150 fans attending Dukes games in order to see if these estimates are accurate. For the sample of 150, the observed frequency of each age category is given in the top row of numbers in the table below. The second row of numbers contains the frequencies expected for a random sample of 150 fans if the Dukes' management's estimates are accurate. The bottom row of numbers contains the following value for each of the age categories. (fo-JE) (observed frequency – Expected frequency)? Expected frequency Part 1 Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your responses to three or more decimal places. Send data to Excel O to 12 13 to 18 19 to 35 36 to 55 Over 55 Total ? Observed frequency 24 26 51 27 22 150 fo Expected frequency 15.00 45.00 37.50 8.067 0.800 2.940 Part 2 Answer the following to summarize the test of the hypothesis that the management's estimates are accurate. Use the 0.05 level of significance for the test. (a) Determine the type of test statistic to use. Type of test statistic: (Choose one) (b) Find the value of the test statistic. (Round your answer to two or more decimal places.) (c) Find the critical value. (Round your answer to two or more decimal places.) (d) Can we conclude that the management's original estimates for the age distribution of fans attending Dukes games are inaccurate? OVes ONo