Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. complete parts a) and b)   Male 15,585 27,149 1417 7504 18,232 16,059 13,929 26,128   Female 24,630 13,872 18,097 17,504 13,480 16,833 16,382 18,222   a. Use a   0.01 significance level to test the claim that among​ couples, males speak fewer words in a day than females.   In this​ example,   μd is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the words spoken by the male minus words spoken by the female. What are the null and alternative hypotheses for the hypothesis​ test? a) identify the test statistic, t? identify the p value? b)construct the confidence interval that could be used for the hypothesis test described in part (a)

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 + ...