Question

A facility for bottling soft drinks uses two fill and seal machines. For quality control purposes, data is collected on these machines to determine if they are filling the soft drinks with the same amount of drink. Based on data from these two machines, they found that a 95% confidence interval for the difference in these machines, population means is (-2.5 mL, 0.3 mL). Using this data, the bottling facility would like to test if there is a difference in the average amount of drink that these machines fill up the bottles. a. Can we make a decision for this hypothesis test at level α-0.05? If so, state the decision and how you determined that. If not, explain why there is not enough information. b. Can we make a decision for this hypothesis test at level a 0.01? If so, state the decision and how you determined that. If not, explain why there is not enough information. c. Can we make a decision for this hypothesis test at level 0.1? If so, state the decision and how you determined that. If not, explain why there is not enough information.

Answer 1

a) Yes, we can make a decision for this hypothesis test at 0.05 level. We reject the null hypothesis of no difference because 0 does not lie in the given 95% confidence interval.

b) No, we cannot make a decision for this hypothesis test at 0.01 level. This is because we need a 99% confidence interval to make a decision and as it will be bigger than a 95% confidence interval, 0 can be inside or outside the interval.

c) Yes, we can make a decision for this hypothesis test at 0.1 level. We reject the null hypothesis of no difference. This is because we need a 90% confidence interval to make a decision and as it will be smaller than a 95% confidence interval, 0 will be outside the interval as it is outside the 95% confidence interval.