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Tanzania [10]
3 years ago
13

The Ohio Department of Agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level. F

or premium grade, 14 out of 105 samples failed. (They did not meet the ASTM specification and the FTC octane posting rule.) How many samples would be needed to create a 99 percent confidence interval that is within 0.02 of the true proportion of premium grade fuel-quality failures?
Mathematics
1 answer:
OlgaM077 [116]3 years ago
4 0

Answer:

The Sample size is 1918.89035

Step-by-step explanation:

Consider the provided information.

It is given that 14 out of 105 samples failed.

Therefore p = 14/105 = 0.13 3... and q=1-0.133=0.867

Samples would be needed to create a 99 percent confidence interval.

Subtract the confidence level from 1, then divide by two.

\frac{(1 -0.99)}{2}=0.005

By standard normal table z=2.5758≈2.58

Calculate the sample size as:

n=\frac{z^2pq}{e^2}

Where,  e is the margin of error,

Substitute the respective values.

n=\frac{(2.58)^2(0.133)(0.867)}{(0.02)^2}=1918.89

Hence, the Sample size is 1918.89035

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