Plastic microparticles are contaminating the world's shorelines and much of the pollution appears to come from...

Plastic microparticles are contaminating the world's shorelines and much of the pollution appears to come from fibers from washing polyester clothes. A study took random samples from ocean beaches. A total of 40 samples of size 250 mL were taken, and the mean number of plastic microparticles of sediment was 18.3 with a standard deviation of 8.2.

What is the variable of interest for this situation? Be specific.
Check the CLT basic requirements for a confidence interval.
Calculate the standard error for a confidence interval and find t* from STATKEY
Write the notation for this situation in terms of shape, center, and spread.
Calculate the margin of error.
Find and interpret a 95% confidence interval for the mean number of polyester microfibers per 250 mL of beach sediment.

Expert Solution

(a) The variable of interest for this situation is the mean number of plastic microparticles of sediment.

(b)

Random: The data come from a well-designed random sample or randomized experiment.
Normal: The sampling distribution of the statistic is approximately Normal.
Independent: Individual observations are independent.

(c) The standard error = s/√n = 8.2/√40 = 1.297

The critical t-value is 2.02.

(d) X ~ N(18.3, 8.2)

(e) The margin of error = t*(s/√n) = 2.02*8.2/√40 = 2.622

(f) The 95% confidence interval for the mean number of polyester microfibers per 250 mL of beach sediment is:

= x t*(s/√n)

= 18.3 2.02*8.2/√40

= (15.678, 20.922)

The 95% confidence interval for the mean number of polyester microfibers per 250 mL of beach sediment is between 15.678 and 20.922.

We are 95% confident that the true mean number of polyester microfibers per 250 mL of beach sediment is between 15.678 and 20.922.

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orchestra answered 1 year ago

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Plastic microparticles are contaminating the world's shorelines and much of the pollution appears to come from...

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