Question

Last rating period, the percentages of viewers watching several channels between 11 p.m. and 11:30 p.m. in a major TV market were as follows:

WDUX (News)	WWTY (News)	WACO (Cheers Reruns)	WTJW (News)	Others
16%	19%	24%	16%	25%

Suppose that in the current rating period, a survey of 2,000 viewers gives the following frequencies:

WDUX (News)	WWTY (News)	WACO (Cheers Reruns)	WTJW (News)	Others
335	495	444	378	348

(a) Show that it is appropriate to carry out a chi-square test using these data.

Each expected value is ≥         

(b) Test to determine whether the viewing shares in the current rating period differ from those in the last rating period at the .10 level of significance. (Round your answer to 3 decimal places.)

χ2χ2          

(Click to select)Do not rejectReject H₀. Conclude viewing shares of the current rating period (Click to select)differdo not differ from those of the last.

Answer 1

a)

each expected value ≥ 5

b)

Chi square test for Goodness of fit  
  
expected frequncy,E = expected proportions*total frequency  
total frequency=   2000

category	observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
WDUX	335	0.1600	320			0.703
WWTY	495	0.1900	380			34.803
WACO	444	0.2400	480			2.700
WTJM	378	0.1600	320			10.513
others	348	0.2500	500			46.208

chi square test statistic,X² = Σ(O-E)²/E =   94.926
level of significance, α=   0.1              
Degree of freedom=k-1=   5   -   1   =   4
                  
P value =   0.0000   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho                  

conclusion: Reject H₀. Conclude viewing shares of the current rating period