A real estate company, We Rent Houses, regularly conducts survey for average rents in Tampa Bay Area. According to its latest survey, the sample mean rent in 2019 was $950 for Pasco County and $1160 in Hillsborough County. Assume the survey sampled rents for 160 rental units in each County. Also, assume the standard deviation in rents based on the survey was $175 in Pasco County and $230 in Hillsborough County. Compute the valued mannually.  a. Calculate a 95% confidence interval for the population mean rent for Hillsborough County. Provide an interpretation of the confidence interval.  b. Calculate a 95% confidence interval for the population mean for Pasco County. Interpret.  c. Is it possible that the population mean rent in Pasco County is higher than that in Hillsborough County? Explain.

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 + ...