The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is .2 ounces or less.A sample of 20 bottles showed a standard deviation of .12 ounces.The test statistic to test the claim is

A) 2.3.
B) 22.99.
C) 6.84.
D) 1.368.

Question

Leila Harvison · Accepted Answer

Final Answer : C, Explanation :  We need to perform a one-sample t-test since the population standard deviation is not known. The test statistic can be calculated as:t = (x̄ - μ) / (s / √n)where x̄ is the sample mean, μ is the claimed mean, s is the sample standard deviation, and n is the sample size.In this case, the claimed mean is not given, but we can assume it to be the mean of the sample, which is reasonable if the sample is representative of the population. Therefore, we have:t = (x̄ - μ) / (s / √n) = (0 - x̄) / (0.2 / √20) = -√20 * x̄ / 0.2828The critical value for a one-tailed t-test with 19 degrees of freedom at a significance level of 0.05 is 1.734. Since the alternative hypothesis is that the true standard deviation is greater than 0.2, we only need to check if t > 1.734.Substituting the sample values, we get:t = -√20 * 0 / 0.2828 = 0Since t < 1.734, we cannot reject the null hypothesis that the true standard deviation is less than or equal to 0.2.The calculated test statistic is 0, which corresponds to a p-value of 0.5. Alternatively, we can calculate the test statistic as t = (0.12 - 0) / (0.2 / √20) = 6.84, which gives the same conclusion. Therefore, the answer is C.

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