The pcb concentration of a fish caught in lake michigan was measured by a technique that is known to result in an error of measurement that is normally distributed with a standard deviation of .08 ppm (parts per million). suppose the results of 10 independent measurements of this fish are 11.2, 12.4, 10.8, 11.6, 12.5, 10.1, 11.0, 12.2, 12.4, 10.6(a) give a 95 percent confidence interval for the pcb level of this fish.(b) give a 95 percent lower confidence interval.(c) give a 95 percent upper confidence interval.

a) The 95% confidence interval would be given by (10.863;12.097)

b)  

c) :

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Part a) Confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

Data: 11.2, 12.4, 10.8, 11.6, 12.5, 10.1, 11.0, 12.2, 12.4, 10.6

In order to calculate the mean and the sample deviation we can use the following formulas:  

(2)  

(3)  

The mean calculated for this case is

The sample deviation calculated

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 95% confidence interval would be given by (10.863;12.097)

Part b) Give a 95 percent lower confidence interval

On this case we want a interval on this form :

So the critical value would be on this case and we can use the following excel code to find it: "=T.INV(1-0.05,9)"

We found the lower limit like this:

And the interval would be:

Part c) Give a 95 percent upper confidence interval.

On this case we want a interval on this form :

So the critical value would be on this case and we can use the following excel code to find it: "=T.INV(1-0.05,9)"

We found the lower limit like this:

And the interval would be:

sine

step-by-step explanation:

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