A recent broadcast of a television show had a 20 share, meaning that among 6000

Question

A recent broadcast of a television show had a 20 share, meaning that among 6000 monitored households with TV sets in use, 20% of them were tuned to this program. Use a 0.01 significance level to test the claim of an advertiser that among the households with TV sets in use, less than 25% were tuned into the program. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

Explanation / Answer

Null hypothesis H0:p=0.25

Alternative hypothesis Ha: p<0.25

Sample size n=6000

Phat=0.20

Test statistics z=(phat-0.25)/sqrt(0.25*(1-0.25)/n)

=(0.20-0.25)/sqrt(0.25*(1-0.25)/6000)

=-8.94

p-value=P(Z<-8.94)=0.0000

As p-value is too small, we reject the null hypothesis and conclude that less than 25% were tuned into the program

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