A report states the average rent for office space in a urban area is $17.75 per square foot. A real estate agent claims this average is incorrect. The agent selected a sample of 23 rental properties and found their mean to be $19.25 per square foot, with a sample standard deviation of $3.45 per square foot. Test the claim at alpha = 0.10. Use the P-value method to evaluate/compare with the given alpha (0.10). For question #18, give your calculated value for "t", rounding to the hundredths place. For question #19 (multiple choice), choose between what two areas your calculated t-value (when converted to P-value) falls. For question #20, answer True or False with regard to rejecting the null hypothesis. Hint: this is a two-tailed 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 + ...
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