Two machines used to fill soft drink containers are being compared. The number of containers filled each minute is counted for 26 minutes for each machine. During the 26 minutes, machine 1 filled an average of 69.2 cans per minute with a sample standard deviation of 2.1 cans per minute, and machine 2 filled an average of 68.5 cans per minute with a sample standard deviation of 3.1 cans per minute. Assume both populations are normally distributed and the population standard deviations are unequal. Can you conclude that machine 1 is faster than machine 2 at the ? =0.05 level? State the relevant hypotheses, compute the test statistic and p-value, and state your conclusion in context. a) Describe what committing a Type I error would be in this situation. b) Describe what committing a Type II error would be in this situation.
Two machines used to fill soft drink containers are being compared. The number
of containers filled each minute is counted for 26 minutes for each machine. During the 26
minutes, machine 1 filled an average of 69.2 cans per minute with a sample standard
deviation of 2.1 cans per minute, and machine 2 filled an average of 68.5 cans per minute
with a sample standard deviation of 3.1 cans per minute. Assume both populations are
normally distributed and the population standard deviations are unequal. Can you conclude
that machine 1 is faster than machine 2 at the ? =0.05 level? State the relevant hypotheses,
compute the test statistic and p-value, and state your conclusion in context.
a) Describe what committing a Type I error would be in this situation.
b) Describe what committing a Type II error would be in this situation.
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