Question

2. In 2004, a team of researchers published a study of contaminants in farmed salmon. Fish from many sources were analyzed for 14 organic contaminants. The study expressed concerns about the level of contaminants found. One of those was the insecticide mirex, which has been shown to be carcinogenic and is suspected to be toxic to the liver, kidneys, and endocrine system. Summaries for the mirex concentrations (in parts per million) in the farmed salmon are: n=150, X ̅=0.0913 ppm, s=0.0495 ppm. (1) What assumptions and conditions must be checked before finding a confidence interval? (2) Find a 95% confidence interval for the mean level of mirex concentrations. Show the formula, not just by Minitab. (3) Interpret this confidence interval. (4) Explain what 95% confidence means.

Answer 1

(1) What assumptions and conditions must be checked before finding a confidence interval?

We must check the assumption that whether the sample is coming from a normally distributed population or not. Also, we must check whether there is any outliers present in the sample data or not.

(2) Find a 95% confidence interval for the mean level of mirex concentrations. Show the formula, not just by Minitab.

The formula for confidence interval for the population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

We are given

Xbar = 0.0913

S = 0.0495

n = 150

Confidence level = 95%

df = n – 1 = 150 – 1 = 149

Critical t value = 1.9760

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 0.0913 ± 1.9760*0.0495/sqrt(150)

Confidence interval = 0.0913 ± 1.9760*0.004041658

Confidence interval = 0.0913 ± 0.0080

Lower limit = 0.0913 - 0.0080 = 0.0833

Upper limit = 0.0913 + 0.0080 = 0.0993

Confidence interval = (0.0833, 0.0993)

(3) Interpret this confidence interval.

We are 95% confident that the population mean for mirex concentrations (in parts per million) in the farmed salmon will lies within 0.0833 and 0.0993.

(4) Explain what 95% confidence means.

95% confidence means about 95% of the times, the population mean will lies within the given confidence interval when we find it by using several samples of same size.