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How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, then dug up the strips and measured the force required to break them. Breaking strength is easy to measure and is a good indicator of decay. Lower strength means the fabric has decayed. For one part of the study, the researcher buried $10$strips of polyester fabric in well-drained soil in the summer. The strips were randomly assigned to two groups: $5$of them were buried for $2$weeks and the other $5$were buried for $16$weeks. Here are the breaking strengths in pounds

Do the data give good evidence that polyester decays more in $16$weeks than in $2$weeks? Carry out an appropriate test to help answer this question .

Step by step solution

01

Given information

Given in the question that,

$\begin{array}{r}{n}_1=90,{\stackrel{炉}{x}}_1=2.95,s_1=0.22\\ n_2=45,{\stackrel{炉}{x}}_2=3.61,s_2=0.19\end{array}$

02

Explanation

According to the given data

$n_1=90,{\stackrel{炉}{x}}_1=2.95,s_1=0.22$

$n_2=45,{\stackrel{炉}{x}}_2=3.61,s_2=0.19$

To construct the confidence interval, follow the procedures supplied by the Ti-83 calculator:

1. Click on STAT$>TESTS>2$-SampTInt

2. Click on Stats and enter the provided data set.

3. Select Polled: No and calculate

4. Press ENTER

The output obtained is

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