he mean family income for a random sample of 700 suburban households in Guinesstowne shows that a 90 percent confidence interval is ($47,250, $62,100). Herman is conducting a test of the null hypothesis H0: µ = 45,000 against the alternative hypothesis Ha: µ ≠ 45,000 at the α = 0.10 level of significance. Does Herman have enough information to conduct a test of the null hypothesis against the alternative? Group of answer choices Yes, because $45,000 is not contained in the 90% confidence interval, the null hypothesis would not be rejected, and it could be concluded that the mean family income is not significantly different from $45,000 at the α = 0.10 level   Yes, because $45,000 is not contained in the 90% confidence interval, the null hypothesis would be rejected in favor of the alternative, and it could be concluded that the mean family income is significantly different from $45,000 at the α = 0.10 level   No, because the value of σ is not known   No, because it is not known whether the data are Normally distributed   No, because the entire data set is needed to do this test

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 + ...