Question

For many years, TV executives used the guideline that 30% of the audience was watching each of the traditional big three prime-time networks and 10% was watching cable stations on a weekday night. A random sample of 600 viewers in the Tampa–St. Petersburg, Florida, area last Monday night showed that 190 homes were tuned in to the ABC affiliate, 195 to the CBS affiliate, and 150 to the NBC affiliate, with the remainder viewing a cable station. At the 0.02 significance level, can we conclude that the guideline is still reasonable? H0: The proportions are as stated. H1: The proportions are not as stated.

a) State the decision rule using 0.02 significance level. (Round your answer to 3 decimal places.)

b) Compute the value of chi-square. (Round your answer to 3 decimal places.)

What is your decision regarding H₀?

reject / do not reject is / is not

H0. Proportion of viewers

as stated.

Answer 1

a)here degree of freedom =categories-1=4-1=3

for 3 degree of freedom and 0.02 level Decision rule: rject Ho if test statitic >9.837

b)applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
ABC	0.300	190.000	180.000		0.556
CBS	0.300	195.000	180.000		1.250
NBC	0.300	150.000	180.000		5.000
Cable	0.100	65.000	60.000		0.417
total	1.000	600	600		7.222

value of chi-square =7.222

decision regarding H0?: do not reject  H0. Proportion of viewers is as stated