Question

Plastic microparticles are contaminating the world’s shorelines, and much of this pollution appears to come from fibers from washing polyester clothes. The worst offender appears to be fleece, and a recent study found that the mean number of polyester fibers discharged into wastewater from washing fleece was 290 fibers per liter of wastewater. Researchers are hoping to reduce the amount of fibers discharged into wastewater by using filters on washing machines. Using a filter, researchers measured 120 samples of wastewater and calculated a 99% confidence interval for the true mean number of polyester fibers in wastewater of (144.702, 169.393).

(a) What multiplier must the researchers have used to obtain this interval?

(b) Calculate the margin of error.

(c) Find the value of the sample statistic.

(d) If everything else where to remain constant, what sample size would the researchers need to collect in order to reduce the margin of error to ten?

(e) Based on the confidence interval, is there evidence to suggest that the filter works? Explain your reasoning.

Answer 1

(a) multiplier=z(0.01/2)=2.5758

(b)lower limit of confidence interval=sample statistic-margin of error=144.702

upper limit of confidence interval=sample statistic-margin of error=169.393

margin of error=(169.393-144.702)/2=12.3455

(c) sample statistic=(169.393+144.702)/2=157.075

(d) n=183

margin of error=z(0.01/2)*sd/sqrt(n)

or, 12.3455=2.5758*sd/sqrt(120)

or, sd=12.3455*sqrt(120)/2.5758=52.50

now margin of error=10,

10=2.5758*52.50/sqrt(n)

or, sqrt(n)=2.5758*52.50/10

or, n=183

(e) since 290 is out of confidence interval((144.702, 169.393), so filter would not work.