Question

Use minitab to solve the following:

A typical cement facility uses a synthetic polymer to filter out dust particles that might be airborne from coking and cement processes. In order to achieve acceptable ambient air conditions, it is necessary to direct the exhaust from the various cement processes to a baghouse (a large vacuum cleaner element). Because the filters in the baghouse undergo harsh conditions, they do not last long. The Baghouse data gives the lifetime (in days) of Polymer filters and Nomex-type filters,

Life	Type
35	Polymer
25	Polymer
28	Polymer
26	Polymer
31	Polymer
34	Polymer
31	Polymer
29	Polymer
33	Polymer
33	Polymer
31	Polymer
27	Polymer
31	Polymer
33	Polymer
28	Polymer
28	Polymer
30	Polymer
33	Polymer
29	Polymer
31	Polymer
26	Polymer
29	Polymer
35	Polymer
32	Polymer
30	Polymer
33	Polymer
30	Polymer
29	Polymer
33	Polymer
33	Polymer
32	Nomex
30	Nomex
30	Nomex
33	Nomex
32	Nomex
32	Nomex
31	Nomex
31	Nomex
29	Nomex
29	Nomex
30	Nomex
33	Nomex
27	Nomex
27	Nomex
32	Nomex
32	Nomex
28	Nomex
27	Nomex
30	Nomex
26	Nomex
30	Nomex
34	Nomex
31	Nomex
26	Nomex
28	Nomex
28	Nomex
28	Nomex
28	Nomex

a.) Completely analyze the differences in the lifetime between the Polymer and Nomex filters. Note that a complete analysis includes stating and checking the assumptions, performing appropriate hypothesis tests using a 0.05 level of significance, writing a clear conclusion that connects with the question asked.

Answer 1

Construct the boxplot for difference In this study, the paired t test is appropriate because the given data compare the lifetimes (in days) of polymer filters to those of Nomex-type filters Excel add-in (PHStat) procedure: Step 1: In EXCEL, Select Add-Ins>PHStat> Descriptive Statistics> Boxplot. Step 2: In Data, select the cell range A1:A30 under Raw Data Cell Range. Step 3: In Input Options, choose Single Group Variable Step 4: In Output Options, enter a Title Step 5: Click OK

Excel add-in (PHStat) output: Boxplot From the graph, it is observed that the distribution of the differences is approximately normally distributed

State the null and alternative hypothesis. Null hypothesis: That is, there are no differences in the lifetime between the Polymer and Nomex filters Alternative hypothesis That is, there are differences in the lifetime between the Polymer and Nomex filters

Excel add-in (PHStat) procedure: Step Add-Ins> PHStat> Two-Sample Tests (Unsummarized Data) Step 2: Choose Paired t Test. Step 3: In Data enter 0 Under Hypothesized Difference. Step 4: Enter 0.05 Under Level of Significance Step 5: Enter A1:A30 Under Population 1 Sample Cell Range. Step 8: Enter B1:B30 Under Population 2 Sample Cell Range. Step 7: Check First cells in both ranges contain label. Step 8:Choose Two-Tail Test Under Test Options 1: In EXCEL Select

Excel add-in (PHStat) output: Paired t Test Data Hypothesized Mean Difference Level of significance 0.05 Intenmediate Calculations Sample Size DBar Degrees of Freedom 29 28 3.1349 0.5821 0.9478 Standard Error t Test Statistic Two-Tail Test Lower Critical Value Upper Critical Value p-Value Do not reject the null hypothesis 2.0484 2.0484 0.3514 From the output, the test statistc is 0.9478 and the p-value is 0.3514
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