Round intermediate steps to four decimal places if necessary. An article describ
ID: 3229279 • Letter: R
Question
Round intermediate steps to four decimal places if necessary. An article describes a study of methods for reducing variance in estimators of the mean inventory on hand for a standard inventory model. Ten replications of an experiment using the method of antithetic variates yielded an average reduction of 10.7% with a standard deviation of 4.2%. Can you conclude that the mean reduction for this method is greater than 10%? Since the P-value is, we conclude that the mean reduction is greater than 10%.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 10
Alternative hypothesis: > 10
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 1.33
DF = n - 1 = 10 - 1
D.F = 9
t = (x - ) / SE
t = 0.527
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 0.527. We use the t Distribution Calculator to find P(t > 0.527) = 0.305
Interpret results. Since the P-value (0.305) is greater than the significance level (0.01), we cannot reject the null hypothesis.
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