6) Tiger-PrimeTM has entered production, and you have been hired as an independe
ID: 3367239 • Letter: 6
Question
6) Tiger-PrimeTM has entered production, and you have been hired as an independent investigator to ensure the company isn't losing money unnecessarily. Rickie is rather concerned about overfilling the bottles (he doesn't care much about under-filling the bottles, because that means more profit). Rickie has given strict instructions that each bottle must contain no more tha Imperial Quart of Tiger-PrimeM (or 1136.52 , but Rickic is American and doesn't know what either "milli" or "tre" mean). The filling machine is set so that each bottle is filled with 136.52 ml of Tiger-PrimeTM with a standard deviation of 13ml. You have been given a sample of 42 bottles, which have an average of 1140.2 ml in them. Is Rickie losing moncy due to over-filling? Calculate with at a-.05Explanation / Answer
Solution:-
6)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u < 1136.52
Alternative hypothesis: u > 1136.52
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 0.05. 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 = 2.00594
DF = n - 1
D.F = 41
t = (x - u) / SE
t = 1.835
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 1.835.
Thus the P-value in this analysis is 0.037
Interpret results. Since the P-value (0.037) is less than the significance level (0.05), we have to reject the null hypothesis.
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