Your small company bus large lots of parts from a manufacturer which you then us
ID: 3044244 • Letter: Y
Question
Your small company bus large lots of parts from a manufacturer which you then use in assembling your product. You are of course concerned that these parts meet your specification, which is weight, which you specified to be a maximum of 12 oz. You then assumed that accepting an average of 11.8 would be acceptable.
a) specify your hypotheses and your alpha and critical value before doing any testing:
b) you have sampled the lot and found the average weight to be 11.7 with a standard deviation of 0.1 oz. your sample size was 15 will you accept lot? Why? show calculations
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 11.8
Alternative hypothesis: < 11.8
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 = 0.02582
DF = n - 1
D.F = 14
t = (x - ) / SE
t = - 3.87
tcritical = - 1.76
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 - 3.87.
Thus the P-value in this analysis is 0.0009.
Interpret results. Since the P-value (0.0009) is less than the significance level (0.05), we have to reject the null hypothesis.
Hence we have to accept the lot.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.