A recent report indicated that families in a certain country typically spend about $175 per week on groceries. To investigate whether families in a certain city typically spend more than $175 per week, an economist selected a random sample of 500 families in the city and found the sample mean to be $176.24. With all conditions for inference met, a hypothesis test resulted in a pp-value of 0.0021. At the significance level of α=0.05α=0.05, which of the following is a correct conclusion?     The pp-value is less than 0.05, and the null hypothesis is rejected. There is convincing statistical evidence that the mean is greater than $175. A The pp-value is less than 0.05, and the null hypothesis is not rejected. There is convincing statistical evidence that the mean is greater than $175. B The pp-value is less than 0.05, and the null hypothesis is not rejected. There is not convincing statistical evidence that the mean is greater than $175. C The pp-value is greater than 0.05, and the null hypothesis is rejected. There is convincing statistical evidence that the mean is greater than $175. D The pp-value is greater than 0.05, and the null hypothesis is not rejected. There is not convincing statistical evidence that the mean is greater than $175.

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 + ...