Question

During the first 13 weeks of the television season, the Saturday evening 8:00 P.M. to 9:00 P.M. audience proportions were recorded as ABC 29%, CBS 27%, NBC 24%, and independents 20%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 92 homes, CBS 64 homes, NBC 86 homes, and independents 58 homes. Test with alpha=.05 to determine whether the viewing audience proportions changed. Round your answers to two decimal places.

what is the Test Statistic?

Answer 1

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=

3

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	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
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