Listed below are measured amounts of lead (in micrograms per cubic motor or mu g

Question

Listed below are measured amounts of lead (in micrograms per cubic motor or mu g/m^3) in the air. The FPA has established an air quality standard for lead of 1 5 mu g/m^3. The measurements shown below were recorded at a building on different days Use the given values to construct a 95% confidence interval estimate of the mean amount of lead in the air Is there anything about this data set suggesting that the confidence interval might not be very good? 5.0 1.00 0.36 0.69 0.72 1.30 What is the confidence interval for the population mean mu? mu g/m^3

Explanation / Answer

Let the given variable is X

Data Given,

x

5.40

1.00

0.36

0.69

0.72

1.30

Formula for confidence interval:

X bar (-/+) E

X bar = sample mean

E = tc * ( s / sqrt (n))

tc is the critical value

s is the sample standard deviation

n is the sample size

X bar = sum of x / n

          

x

5.40

1.00

0.36

0.69

0.72

1.30

Total =

9.47

X bar = 9.47 / 6 = 1.5783

s = sqrt (sum of ( x – x bar )^2/(n-1))

  

x

( x - x bar )

( x - x bar )^2

5.40

3.8217

14.605

1.00

-0.5783

0.334

0.36

-1.2183

1.484

0.69

-0.8883

0.789

0.72

-0.8583

0.737

1.30

-0.2783

0.077

Total =

9.47

18.027

s = sqrt (18.027/(6-1))

= 1.8988

Degrees of freedom = n – 1 = 6 – 1 = 5

The critical t we get from t table for 5% level of significance as 2.571

E = 2.571 * (1.8988 / sqrt (6))

1.5783 (-/+) 1.9930

=-0.415 and 3.571

Answer:

-0.415 < µ < 3.571

If we use excel we get,

-0.414 < µ < 3.571

Option B: Yes, the value of 5.40 appears to be an outlier.

x

5.40

1.00

0.36

0.69

0.72

1.30

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