A university IT centre has upgraded its hardware in their servers used by students submitting their work to the LMS during times of peak congestion. Some statistics were collected in order to evaluate the performance of the new hardware. Before the upgrade was made, a trial submission was made on a random selection of 32 servers in the cluster during a busy time. The mean delay between clicking "Submit" and the submission being uploaded and saved was 5.3 seconds, with standard deviation 0.9 seconds. Following the upgrade, the same trial submission was made on the same 32 servers, yielding a mean delay of 4.9 seconds with standard deviation of 0.8 seconds. The mean of the differences of these delay times was -0.40 seconds with standard deviation of 0.32 seconds. 1. Carry out a hypothesis test to evaluate whether the hardware upgrade made any difference to delay times for submissions. Use the 5% level of significance and a p value decision rule.

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A university IT centre has upgraded its hardware in their servers used by students
submitting their work to the LMS during times of peak congestion. Some statistics
were collected in order to evaluate the performance of the new hardware.
Before the upgrade was made, a trial submission was made on a random selection
of 32 servers in the cluster during a busy time. The mean delay between clicking
"Submit" and the submission being uploaded and saved was 5.3 seconds, with
standard deviation 0.9 seconds. Following the upgrade, the same trial submission
was made on the same 32 servers, yielding a mean delay of 4.9 seconds with
standard deviation of 0.8 seconds. The mean of the differences of these delay times
was -0.40 seconds with standard deviation of 0.32 seconds.
1. Carry out a hypothesis test to evaluate whether the hardware upgrade made
any difference to delay times for submissions. Use the 5% level of significance
and a p value decision rule.
Include
(a) statement of hypotheses (including definition of any notation)
(b) brief justification of testing approach chosen
(c) test statistics and decision rule
(d) decision of the test and brief interpretation
2. Compute a 99% confidence interval for the change in the mean delay as a result
of the hardware upgrade.
Transcribed Image Text:A university IT centre has upgraded its hardware in their servers used by students submitting their work to the LMS during times of peak congestion. Some statistics were collected in order to evaluate the performance of the new hardware. Before the upgrade was made, a trial submission was made on a random selection of 32 servers in the cluster during a busy time. The mean delay between clicking "Submit" and the submission being uploaded and saved was 5.3 seconds, with standard deviation 0.9 seconds. Following the upgrade, the same trial submission was made on the same 32 servers, yielding a mean delay of 4.9 seconds with standard deviation of 0.8 seconds. The mean of the differences of these delay times was -0.40 seconds with standard deviation of 0.32 seconds. 1. Carry out a hypothesis test to evaluate whether the hardware upgrade made any difference to delay times for submissions. Use the 5% level of significance and a p value decision rule. Include (a) statement of hypotheses (including definition of any notation) (b) brief justification of testing approach chosen (c) test statistics and decision rule (d) decision of the test and brief interpretation 2. Compute a 99% confidence interval for the change in the mean delay as a result of the hardware upgrade.
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