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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?

Answer & Explanation Solved by verified expert
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= 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
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