The net weights of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample filled by a similar machine manufactured by Orno, Inc., are (in grams): Testing the claim at the 0.05 level the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine, what is the critical value?
A) -1.96
B) -2.837
C) -6.271
D) +3.674
E) +1.782

Question

The net weights of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample filled by a similar machine manufactured by Orno, Inc., are (in grams):  Testing the claim at the 0.05 level the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine, what is the critical value?
A) -1.96 
B) -2.837 
C) -6.271 
D) +3.674 
E) +1.782

Quizplus · Accepted Answer

Since we are testing the claim at a 0.05 level of significance and the null hypothesis is that the mean weight of the bottles filled by the Orno machine is equal to or less than the mean weight of the bottles filled by the Edne machine, this is a one-tailed test with a critical value of +1.645. However, since the alternative hypothesis is that the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine, we need to use the upper tail critical value, which is +1.645. However, since the sample size is small (less than 30), we need to use the t-distribution instead of the z-distribution, which gives a critical value of +1.782 (rounded to three decimal places). Therefore, the answer is E.

The Net Weights of a Sample of Bottles Filled by a Machine