For the problems below, use the appropriate t-test. Regardless of the type of t-
ID: 3375955 • Letter: F
Question
For the problems below, use the appropriate t-test. Regardless of the type of t-test you use (one- sample, two-paired-sample, two-independent-sample), you need to decide on directionality (lower-tail, upper-tail, two-tail), and this decision should be based on the text of the problem. Consider an experiment designed to evaluate a new process for producing synthetic diamonds.A study of the process costs shows that the average weight of the diamonds must be greater than.5 carat (1 carat = 200 mg) for the process to profitable. A random sample of six diamonds was drawn. The weights are .46, .61,.52,.48, .57, .54. Do these weights provide sufficient evidence that mean diamond weight produced by this process exceeds .5 carat? 1.Explanation / Answer
Here we have to test the hypothesis that,
H0 : mu = 0.5 carat Vs H1 : mu > 0.5 carat
where mu is population mean diamond weight.
Assume alpha = level of significance = 0.05
This is the upper tail test since alternative hypothesis contains > sign.
Sample size (n) = 6
SO we use one sample t-test.
One sample t-test in SAS :
0.46 0.61 0.52 0.48 0.57 0.54
Output is :
One-Sample T: weights
Test of ? = 0.5 vs > 0.5
Variable N Mean StDev SE Mean 95% Lower Bound T P
weights 6 0.5300 0.0559 0.0228 0.4840 1.32 0.123
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : There is not sufficient evidence to say that mean diamond weight produced by this process exceeds.