Question

The production manager of Twin Forks Inc., has asked your assistance in evaluating a modified box production process. When the process is operating properly, the process produces boxes whose weights are normally distributed with a population mean of 5 ounces, population standard deviation of 0.1 ounce and the population distribution is normal. A new raw-material supplier was used for a recent production run, and the manager wants to know if that change has resulted in a lowering of the mean weight of the boxes. A random sample of 16 observations are taken and their average weight was 4.962.

a. Test at 5% significance level to check if the new material has lowered mean weight of boxes using p-value approach.

b. Test at 10% significance level to check if the new material has lowered mean weight of boxes using p-value approach.

c. Does you result change when significance level changes. Why?

Answer key: Left sided test.

Z stat = -1.52

P value (z<-1.52) = 0.0643

a) α=0.05 since α < p value. Do not reject null hypothesis

b) α=0.1 since α > p value. Reject null hypothesis

(Please show with figure, decision rule and decision.)

Answer 1

Given - Mas :01 n.16 Ž: 2.962 I Ho: M:s Hai Mago (left tailed) X-M 2: 4.982-5 0:1 (VT6 -0.038 :-1-57 0.025 0.0642 P-value a ) 2=0.05 * 10-05) Hai Mas P-value 10.0642) 2010.05 Do not reject Ho -1.52

0:00 h when critical af values are -1.65 I value. (61-65) Reject Ho -1.52 > 6-1.65) Dondt reject. Ho ponot veject Home Reject Ho -1.65 -1.52 b ) P-value (0.0642) 2010.1) Reject Ho. 2:0.10 critical values are. -1:28

calculated 2. les than -1- 38 사 Reject Ho lisa (-1-28) Reject He Reject Donot fejectha 2