In a packing plant, a machine packs cartons with jars. The manufacturer of a new

Question

In a packing plant, a machine packs cartons with jars. The manufacturer of a new packing machine claims that the new machine will pack faster on the average than the machine currently used. To test that hypothesis, the times it takes each machine to pack ten cartons are recorded. The results, in seconds, are shown in the following table.
New machine(data on left) || Old machine(data on right)
42.1 41.3 42.4 43.2 41.8 ||42.7 43.8 42.5 43.1 44.0
41.0 41.8 42.8 42.3 42.7 ||43.6 43.3 43.5 41.7 44.1
a)Do the data provide sufficient evidence to conclude that, on the average, the new machine packs faster? Perform the required hypothesis test at the 5% level of significance.

b)State and check the assumptions of the above procedure you used in part (a)?

c)Compute a 99% confidence interval for the difference between the mean packing times of the two types of machines.

Explanation / Answer

Let denote the mean for the new machine and denote the mean for the old machine. Step 1. Ho: - = 0, Ha: - < 0 Step 2. Significance level: = 0.05. Step 3. Compute the t-statistic: Step 4. Critical value: Left-tailed test Critical value = - = - t0.05 Degrees of freedom = 10 + 10 - 2 = 18 - t0.05 = -1.734 Rejection region t < -1.734 Step 5. Check to see if the value of the test statistic falls in the rejection region and decide whether to reject Ho. t* = -3.40 < -1.734 Reject Ho at = 0.05 Step 6. State the conclusion in words. At 5% level of significance, the data provide sufficient evidence that the new machine packs faster than the old machine on average. Question #2 Continuing from the previous example, give a 99% confidence interval for the difference between the mean time it takes the new machine to pack ten cartons and the mean time it takes the present machine to pack ten cartons. Step 1. = 0.01, = t0.005 = 2.878, where the degrees of freedom are 18. Step 2. The 99% confidence interval is (-2.01, -0.17). Interpret the above result: We are 99% confident that - is between -2.01 and -0.17.

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