The news program for KOPE, the local televisoin station, claims to have 40% of t

Question

The news program for KOPE, the local televisoin station, claims to have 40% of the market. A random sample of 500 viewers conducted by an independent testing agency found 192 who claim to watch KOPE news program on a regular basis.

A. Find the p-value for testing the hypothesis that the news program for KOPE does not have at least 40% of the market, as it claims.

B. Is there sufficient evidence to reject the hypothesis that KOPE does not have at least 40% of the market at the significance level of 0.05?

Please show the work for all of these questions.

Thanks

Explanation / Answer

a)here null hypothesis:Ho: p>=0.40

alternate hypothesis:Ha: p<0.40

for p=0.4 and n=500

therefore std errror =(p*(1-p)/n)1/2 =0.0219

sample proportion phat=192/500=0.384

test statistic z=(phat-p)/std error =(0.384-0.40)/0.0219=-0.7306

for abve test statistic and left tailed test p vlaue =0.2325

b) as p value is higher then 0.05 level we do not have  sufficient evidence to reject the hypothesis that KOPE does not have at least 40% of the market at the significance level of 0.05.

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