A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one​ minute?   80 89 51 72 51 36 66 72 78 55 74 81 104 101 76   Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?     A. H0​: μ=60 seconds H1​: μ<60 seconds   B. H0​: μ=60 seconds H1​: μ>60 seconds   C. H0​: μ≠60 seconds H1​: μ=60 seconds   D. H0​: μ=60 seconds H1​: μ≠60 seconds Determine the test statistic.     Determine the​ P-value.   State the final conclusion that addresses the original claim.     Fail to reject Reject H0. There is   sufficient not sufficient evidence to conclude that the original claim that the mean of the population of estimates is 60 seconds   is is not correct. It   appears does not appear ​that, as a​ group, the students are reasonably good at estimating one minute

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 + ...