The U.S. Department of Transportation requires tire manufactures to provide performance on tire sidewalls to help prospective buyers make their purchasing decisions. One very important place of information is the tread wear index, which indicates the tire’s resistance of tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100. A consumer organization wants to test the actual tread wear index of a brand name of tires that claims “graded 200� on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4. a. Is three evidence that the population mean tread wear index is different from 200? (Use a 0.05 level of significance.) b. Determine the p -value and interpret its meaning.
The U.S. Department of Transportation requires tire manufactures to provide performance on tire sidewalls to help prospective buyers make their purchasing decisions. One very important place of information is the tread wear index, which indicates the tire’s resistance of tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100. A consumer organization wants to test the actual tread wear index of a brand name of tires that claims “graded 200� on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4. a. Is three evidence that the population mean tread wear index is different from 200? (Use a 0.05 level of significance.) b. Determine the p -value and interpret its meaning.
Solution Summary: The author demonstrates the five-step p-value approach to determine whether the population mean tread wear index is different from 200.
The U.S. Department of Transportation requires tire manufactures to provide performance on tire sidewalls to help prospective buyers make their purchasing decisions. One very important place of information is the tread wear index, which indicates the tire’s resistance of tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100.
A consumer organization wants to test the actual tread wear index of a brand name of tires that claims “graded 200� on the sidewall of the tire. A random sample of
n
=
18
indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4.
a. Is three evidence that the population mean tread wear index is different from 200? (Use a 0.05 level of significance.)
b. Determine the p-value and interpret its meaning.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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