Question

In a packing plant, one of the machines packs jars into a box. A sales rep for a packing machine manufacturer comes into the plant saying that a new machine he is selling will pack the jars faster than the old machine. To test this claim, each machine is timed for how long it takes to pack 10 cartons of jars at randomly chosen times. Given a 95% confidence interval of (-6.85, 0.34) for the true difference in average times to pack the jars (old machine - new machine), what can you conclude from this interval?
a. We are 90% confident that the average packing time of the new machine is greater than the old machine. The sales rep does not appear to be telling the truth.
b. We do not have enough information to make a conclusion.
c. We are 90% confident that the difference between the two sample means falls within the interval.
d. We are 90% confident that the average packing time of the old machine is greater than the new machine. The sales rep appears to be correct.
e. There is no significant difference between the average packing time of the two machines. The sales rep does not appear to be telling the truth.

Answer 1

Answer:

b. We do not have enough information to make a conclusion.

Step-by-step explanation:

For testing difference of means our null hypothesis and alternative hypothesis is

H0: There is no significant difference between the average packing time of old machine and new machine i.e. μold-μnew=0.

Ha:There is significant difference between the average packing time of old machine and new machine i.e. μold-μnew≠0.

When the confidence contains the null values then there is no significant difference exists. Here the specified null value is 0. A 95% confidence interval (-6.85, 0.34) shows that it contains null value so, there is no significant difference between the average packing time of the two machines at 5% level of significance.  This results is for 95% confidence interval. For 90% confidence interval result may vary and we don't have sufficient information given to compute 90% confidence interval.