A recent broadcast of a television show had a 10 share, meaning that among 6000

Question

A recent broadcast of a television show had a 10 share, meaning that among 6000 monitored households with TV sets in use, 10% 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 15% were tuned into the program. Use the P-value method. Use the normal distribution as anapproximation of the binomial distribution

A) Identify the null hypothesis, and alternative hypothesis

B) test statistic z= (round to nearest 2 decimal places)

C) P-value (4 decimal places)

D) make a conclusion about the null hypothesis (reject or fail to reject, is or is not sufficeint evedince to support the claim of 15%)

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.15
HA : p < 0.15

Hypothesis test results:

Hence,

a) Ho: p = 0.15

Ha: p < 0.15

b) z = -10.85

c) P-value = 0.0000

d) Reject the null hypothesis; is sufficient evidence to support the claim

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