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An alcohol brewery firm claims that the proportion of alcohol in their new drink is at most 10 percent.A random sample of 100 bottles of the drink were selected and found to consist of 9 percent alcohol.
-What conclusions can be drawn using a level of significance equal to 0.10?
A)Since the p-value equals 0.9965,fail to reject the null hypothesis and conclude that the proportion of alcohol is not greater than 10 percent.
B)Since the p-value equals 0.6293 fail to reject the null hypothesis and conclude that the proportion of alcohol is not greater than 10 percent.
C)Since the p-value equals 0.0485,reject the null hypothesis and conclude that that the proportion of alcohol is not less than 10 percent.
D)Since the p-value equals 0.1977,reject the null hypothesis and conclude that that the proportion of alcohol is less than 10 percent.

Question

Quizplus · Accepted Answer

We need to perform a one-tailed hypothesis test with a null hypothesis of p <= 0.10 and an alternative hypothesis of p > 0.10. Using a normal approximation to the binomial distribution, we can calculate the test statistic and the corresponding p-value. With a sample size of 100, the test statistic is z = (0.09 - 0.10)/sqrt(0.10*(1-0.10)/100) = -1.41. The p-value for this test is P(Z > -1.41) = 0.0793 (from a standard normal distribution table or calculator). Since the p-value is greater than the level of significance of 0.10, we fail to reject the null hypothesis and conclude that the proportion of alcohol is not greater than 10 percent. Therefore, the best choice is B.

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