Question

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

160

fans attending Dukes games in order to see if these estimates are accurate. The observed frequencies in the sample of

160

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

160

fans if the Dukes' management's estimates are accurate. The bottom row of numbers in Table 1 contains the values

−fOfE2
fE

for each of the age categories.

Fill in the missing values of Table 1. Then, using the

0.10

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  

−fOfE2fE

responses in Table 1 to at least three decimal places. Round your responses in Table 2 as specified.

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Table 1: Information about the Sample
	Age group
	0 to 12	13 to 18	19 to 35	36 to 55	Over 55	Total
ObservedfreqfO	24	22	55	28	31	160
ExpectedfreqfE		16.00	48.00		32.00
−fOfE2fE		2.250	1.021		0.031
Table 2: Summary of the Hypothesis Test
The type of test statistic:			(Choose one)ZtChi squareF
The value of the test statistic: (Round your answer to at least two decimal places.)
The p-value: (Round your answer to at least three decimal places.)
Can we conclude that the management's original estimates for the age distribution of fans attending Dukes games are inaccurate? Use the 0.10 level of significance.					Yes	No

Answer 1

Table 1: Information about the Sample Age group 0 to 12 13 to 18 19 to 35 36 to 55 Over 55 Total ObservedfreqfO 24 22 55 28 31 160 ExpectedfreqfE =160*15/100 = 24 16.00 48.00 =25*160/100 =40 32.00 −fOfE2fE 0 2.250 1.021 3.6 0.031 6.90208 Table 2: Summary of the Hypothesis Test The type of test statistic: Chi square The value of the test statistic: (Round your answer to at least two decimal places.) 6.90 The p-value: (Round your answer to at least three decimal places.) 0.141 Can we conclude that the management's original estimates for the age distribution of fans attending Dukes games are inaccurate? Use the 0.10 level of significance. No