In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data
Were obtained: State a conclusion using the $\alpha = 0.05$ level of significance.
A) Do not reject $H _ { 0 }$ . There is insufficient evidence to conclude that the mean Difference differs from zero.
B) Reject $H _ { 0 }$ . The mean difference appears to differ from zero.

Question

In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data
Were obtained:  State a conclusion using the $\alpha = 0.05$ level of significance.
A) Do not reject $H _ { 0 }$ . There is insufficient evidence to conclude that the mean Difference differs from zero. 
B) Reject $H _ { 0 }$ . The mean difference appears to differ from zero.

Quizplus · Accepted Answer

By conducting a two-sample t-test with a significance level of 0.05, we obtain a p-value of 0.041. Since the p-value is less than the significance level, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that there is a systematic difference between the weights obtained with the two different mass balances. Therefore, the best choice is B.

In an Experiment to Determine Whether There Is a Systematic α=0.05\alpha = 0.05α=0.05

In an Experiment to Determine Whether There Is a Systematic $\alpha = 0.05$