1. Quality in production can be measured by both the mean and the variance. When there is a lot of variation, there is l
Posted: Mon Nov 15, 2021 12:15 pm
1. Quality in production can be measured by both the mean and
the variance. When there is a lot of variation, there is less
precision and there is a lot of room for improvement. For instance,
a factory producing bags has a target weight for its bags (3.5
lbs). It knows, however, that in the process, some bags end up
weighing more than others. Automation has allowed factories to be
more precise. Yet, there is still much that can be done to get
these machines to be more precise. The company has two different
machines. Each follows a slightly different sewing process. The
company is testing whether machine 1 is very reliable. It considers
the machine reliable if the weight for the final product varies
with a standard deviation of 0.20 lbs or less. If it the variation
is greater, the machine is a lot less precise than one would
desire, and the company may have to look alternatives.
Periodically, the company looks at samples of bags, weighs them,
and checks to see if the sample provides evidence that they are not
only meeting the weight target (on average), but also the precision
target. The excel file contains weight data for two samples of bags
produced by two different machines. Using the sample, check to see
if there is enough statistical evidence suggesting that machine 1
is missing the precision target.
(a) State the null and alternative hypotheses
(b) Report the sample variation used for the hypothesis test
(c) Report the test statistic
(d) Use the p-value approach to determine if there is
statistical evidence of imprecision.
2. Using the sample data for the two machines, determine if
there is any statistically significant difference in machine
precision. In other words, determine if the variances in bag
weights are different between the two machines.
DATA:
the variance. When there is a lot of variation, there is less
precision and there is a lot of room for improvement. For instance,
a factory producing bags has a target weight for its bags (3.5
lbs). It knows, however, that in the process, some bags end up
weighing more than others. Automation has allowed factories to be
more precise. Yet, there is still much that can be done to get
these machines to be more precise. The company has two different
machines. Each follows a slightly different sewing process. The
company is testing whether machine 1 is very reliable. It considers
the machine reliable if the weight for the final product varies
with a standard deviation of 0.20 lbs or less. If it the variation
is greater, the machine is a lot less precise than one would
desire, and the company may have to look alternatives.
Periodically, the company looks at samples of bags, weighs them,
and checks to see if the sample provides evidence that they are not
only meeting the weight target (on average), but also the precision
target. The excel file contains weight data for two samples of bags
produced by two different machines. Using the sample, check to see
if there is enough statistical evidence suggesting that machine 1
is missing the precision target.
(a) State the null and alternative hypotheses
(b) Report the sample variation used for the hypothesis test
(c) Report the test statistic
(d) Use the p-value approach to determine if there is
statistical evidence of imprecision.
2. Using the sample data for the two machines, determine if
there is any statistically significant difference in machine
precision. In other words, determine if the variances in bag
weights are different between the two machines.
DATA: