SOLUTION: The standard deviation of the pollution by-products released in the burning of 1 gallon of gas is 2.3 ounces. A random sample of 20 automobiles tested produced a standard deviation

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Question 1188837: The standard deviation of the pollution by-products released in the burning of 1 gallon of gas is 2.3 ounces. A random sample of 20 automobiles tested produced a standard deviation of 1.9 ounces. Is the standard deviation really less than previously thought? Use α = 0.05.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
i'm not sure if this is right, but here goes.
the standard deviation for the population is assumed to be 2.3 ounces.
with a sample size of 20, the standarfd error is 2.3 / sqrt(20) = .514296 rounded to 6 decimal places.
z-score = (x - m) / s
x is the mean of the sample.
m is the mean of the population.
s is the standard error.
formula becomes:
z = (1.9 - 2.3) / .514296 = -.77776 rounded to 5 decimal places.
critical z-score at one-tailed signjificance level of .05 is equal to -1.645.
since the test z-score is less than that, there is not sufficient information to say that the population standard deviation is less than 2.3.