During the first 13 weeks of the television season, the Saturday evening 8:00 P.M. to 9:00...

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During the first 13 weeks of the television season, the Saturdayevening 8:00 P.M. to 9:00 P.M. audience proportions were recordedas ABC 29%, CBS 27%, NBC 24%, and independents 20%. A sample of 300homes two weeks after a Saturday night schedule revision yieldedthe following viewing audience data: ABC 92 homes, CBS 64 homes,NBC 86 homes, and independents 58 homes. Test with alpha=.05 todetermine whether the viewing audience proportions changed. Roundyour answers to two decimal places.
what is the Test Statistic?

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3.7 Ratings (298 Votes)

null hypothesis: Ho:Distribution of viewing audience proportions is same as stated,

Alternate hypothesis: Ha:Distribution of viewing audience proportions has changed from as stated

degree of freedom =categories-1=

for 0.05 level and 3 degree of freedom :rejection region =

7.815

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	O_i	E_i=total*p	R²_i=(O_i-E_i)/?E_i	R²_i=(O_i-E_i)²/E_i
ABC	0.290	92	87.00	0.54	0.287
CBS	0.270	64	81.00	-1.89	3.568
NBC	0.240	86	72.00	1.65	2.722
independent	0.200	58	60.00	-0.26	0.067
total	1.000	300	300		6.644

Test Statistic X²=6.64

as test statistic is not in rejection region we can not conclude at 0.05 level that Distribution of viewing audience proportions has changed from as stated

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