his Question: 7 pts This Test: 100 pts A recent broadcast of a television show h
ID: 2948170 • Letter: H
Question
his Question: 7 pts This Test: 100 pts A recent broadcast of a television show had a 10 s are meaning that among 500 monitored households with T/ sets in use 10% of hem were tuned to this program. Use a 001 significance level to test the claim of an ad t ser that among te households with TV sets n use, less than 25% were tuned into the p ogram identify the null hypothesis, altermative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final condlusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution. Identify the null and alternative hypotheses. Choose the correct answer below O B. Ho:p=0.75 H: p0.25 OF. Ho P 0.25 H, p0.75 OE. HoP 0.25 H1: p #025 The test statistic is (Round to two decimal places as needed.) The P-value is?(Round to four decimal places as needed.) Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim. Ho There suficient evidence to support the claim that less than 25% of the TV sets in use were tuned to the program.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.25
Alternative hypothesis: P < 0.25
Note that these hypotheses constitute a one-tailed test.
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 (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.00612
z = (p - P) / S.D
z = - 24.51
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 one-tailed test, the P-value is the probability that the z-score is less than -24.51.
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 cannot accept the null hypothesis.
Reject H0, there is sufficient evidence to support the claim that less than 25% of the TVs sets in use were tuned to the program.
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