A recent broadcast of a television show had a 10 share, meaning that among 5000
ID: 3275831 • Letter: A
Question
A recent broadcast of a television show had a 10 share, meaning that among 5000 monitored households with TV sets in use, 10 % of them were turned 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 20% were tuned into the program. Identify the null hypothesis, test statistic, P- value, conclusion about the null hypothesis, and final conclusion that the addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
Identify the null hypothesis. choose the correct answer below.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.20
Alternative hypothesis: P 0.20
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.00569
z = (p - P) /
z = - 17 .6
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than -17.6 or greater than 17.6.
Thus, the P-value = less than 0.0001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that among the households with TV sets in use 20% were tuned into the program.