Question

2) Listed below are the measured amounts of lead (in micrograms per cubic meter) in the air. The measurements shown below were recorded at Building 5 of the World Trade Center site on different days following Sept 11, 2001. After the collapse of the two World Trade Center buildings, there was considerable concern about the quality of the air. Use a 0.05 significance level to test the claim that the sample is from a population with a mean greater than the EPA standard of 1.5. Is there anything about this data set suggesting that the assumption of a normally distributed population might not be valid? Explain.

5.40 I 1.10 I 0.42 I 0.73 I 0.48 I 1.10

Answer 1

Solution:

One sample t-test

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: the sample is from a population with a mean equal to the EPA standard of 1.5.

Alternative hypothesis: Ha: the sample is from a population with a mean greater than the EPA standard of 1.5.

H0: µ =1.5 versus Ha: µ > 1.5

This is an upper tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 1.5

Xbar = 1.538333333

S = 1.914203925

n = 6

df = n – 1 = 5

α = 0.05

Critical value = 2.0150

(by using t-table or excel)

t = (1.538333333 - 1.5)/[ 1.914203925/sqrt(6)]

t = 0.0491

P-value = 0.4814

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the sample is from a population with a mean greater than the EPA standard of 1.5.

This data set suggesting that the assumption of a normally distributed population might not be valid because sample size is very small.

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