18.38 How strong are durable press fabrics? "Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. A study compared the breaking strength of fabrics treated by two commercial durable press processes. Five swatches of the same fabric were assigned at random to each process. Here are the data, in pounds of pull needed to tear the fabric: 20 Permafresh 29.9 30.7 30.0 29.5 Hylite 28.8 23.9 27.0 22.1 27.6 24.2 Is there good evidence that the two processes result in different mean breaking strengths? (a) Do the sample means suggest that one of the processes is superior in breaking strength? (b) Make stemplots for both samples. The Permafresh sample contains a mild out- lier. With just 5 observations per group, we worry that this outlier will affect our conclusions. (c) Test the hypothesis Ho: ₁ = ₂ against the two-sided alternative twice: once using all the data and again without the outlier in the Permafresh sam- ple. Do the two tests lead to similar conclusions? Can we safely conclude that one treatment has significantly higher mean breaking strength than the other?

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## How Strong are Durable Press Fabrics?

"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. A study compared the breaking strength of fabrics treated by two commercial durable press processes. Five swatches of the same fabric were assigned at random to each process. Here are the data, in pounds of pull needed to tear the fabric:

| Permafresh | 29.9 | 30.7 | 30.0 | 29.5 | 27.6 |
|------------|------|------|------|------|------|
| Hylite     | 28.8 | 23.9 | 27.0 | 22.1 | 24.2 |

### Questions

1. **Is there good evidence that the two processes result in different mean breaking strengths?**

   (a) Do the sample means suggest that one of the processes is superior in breaking strength?

   (b) Make stemplots for both samples. The Permafresh sample contains a mild outlier. With just 5 observations per group, we worry that this outlier will affect our conclusions.

   (c) Test the hypothesis \( H_0: \mu_1 = \mu_2 \) against the two-sided alternative twice: once using all the data and again without the outlier in the Permafresh sample. Do the two tests lead to similar conclusions? Can we safely conclude that one treatment has significantly higher mean breaking strength than the other?
Transcribed Image Text:## How Strong are Durable Press Fabrics? "Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. A study compared the breaking strength of fabrics treated by two commercial durable press processes. Five swatches of the same fabric were assigned at random to each process. Here are the data, in pounds of pull needed to tear the fabric: | Permafresh | 29.9 | 30.7 | 30.0 | 29.5 | 27.6 | |------------|------|------|------|------|------| | Hylite | 28.8 | 23.9 | 27.0 | 22.1 | 24.2 | ### Questions 1. **Is there good evidence that the two processes result in different mean breaking strengths?** (a) Do the sample means suggest that one of the processes is superior in breaking strength? (b) Make stemplots for both samples. The Permafresh sample contains a mild outlier. With just 5 observations per group, we worry that this outlier will affect our conclusions. (c) Test the hypothesis \( H_0: \mu_1 = \mu_2 \) against the two-sided alternative twice: once using all the data and again without the outlier in the Permafresh sample. Do the two tests lead to similar conclusions? Can we safely conclude that one treatment has significantly higher mean breaking strength than the other?
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