Question

How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in thes oil 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 is decayed. In part of the study researchers buried 10 strips of polyester fabric in well-drained soil in the summer. Five of the strips, chosen at random, were dug up after 2 weeks; the other 5 were dug up after 16 weeks. . Here are the data (in pounds of breaking strength): Sample 1 (2 weeks) 118 126 126 120 129 Sample 2 (16 weeks) 124 98 110 140 110 These data can be downloaded: Minitab data Excel or text data Find a 95% confidence interval for the difference in the mean breaking strengths, specifically the mean 2-week breaking strength minus the mean 16-week breaking strength.

Answer 1

Answer:

no enough evidence to draw up a conclusion

Step-by-step explanation:

Data:

let: $\mu _{1}$ = decay after 2 weeks

    $\mu _{2}$ = decay after 16 weeks

Making the hypotheses:

Null hypothesis; $H_{o} = \mu _{1} - \mu _{2} = 0$

the deviation = 0.05

the standard difference  = 4

Conditions:

The normal distribution curve can be plotted on a graph and the plot shows that the distribution is a skewed distribution.

Then,

$t = \frac{(123.8-16.4)-0}{\sqrt{\frac{4.6^{2} }{5}+\frac{16.09^{2} }{5} } } \\ = 0.989$

Therefore, it can be concluded that 0.1983 > 0.05. This presents our failure to reject the null hypothesis.

Thus, there is not enough evidence to conclude that polyester decays more in less than 2 weeks.