The mean annual incomes of certified welders are normally distributed with a mean of $51,050 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $51,050 annually. A sample of 100 welders is taken and the mean annual income of the sample is $51,350. If the level of significance is 0.05, what conclusion should be drawn?
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Do not reject the null hypothesis as the test statistic is less than the critical value of z.
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Do not reject the null hypothesis as the test statistic is less than the critical value of t.
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Reject the null hypothesis as the test statistic is greater than the critical value of t.
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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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