Question

Please Please include work so I can understand how to process :)

Three way catalytic converters have been installed in new vehicles in oder to reduce pollutants from motor vehicles exhaust emissions. However, these converters unintentionally increase the level of ammonia in the air. Environmental Science and Technology published a study on the ammonia levels near the exit ramp of a San Francisco highway tunnel. The data in the next table represent daily ammonia concentrations ( parts per million) on eight randomly selected days during afternoon drive time in the summer of 1999

X= 1.53, 1.50, 1.37, 1.51, 1.55, 1.42, 1.41, 1.48

1) conduct a hypothesis test to determine if the true mean daily

ammonia concentration in air for the selected exit

ramp of a San Francisco highway in summer 1999

was greater than a public health threshold set at

1.44 ppm. Specifically,

a)

Give the null and alternative hypotheses

b)

Compute the test statistic

c)

Describe Type I error for this test

d)

Describe Type II error for this test

e)

Provide the critical value

f)

Conclude using words your grandma would

understand

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ <= 1.44
Alternative Hypothesis, Ha: μ > 1.44

b)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1.47 - 1.44)/(0.064/sqrt(8))
t = 1.326

c)
Type I error occurs here if we conclude that the mean ammonia concentration in air is greater than 1.44 ppm however the true mean ammonia concentration is less than 1.44 ppm

d)
Type II error occurs here if we fail to reject the null hypothesis that the mean ammonia concentration is greater than 1.4 ppm however the true mean ammonia concentration is greater than 1.44 ppm

e)
Rejection Region
This is right tailed test, for α = 0.05 and df = 7
Critical value of t is 1.895.

f)
Hence reject H0 if t > 1.895
Fail to reject H0
There is not sufficient evidence to conclude that the mean ammonia concentration is greater than 1.44 ppm