A local chess club claims that the length of time to play a game has a mean of 43 minutes or more. Write sentences describing type I and type II errors for a hypothesis test of this claim. A type I error will occur if the actual mean of the length of time to play a game is ▼   equal to less than or equal to not equal to greater than or equal to greater than less than 43 ​minutes, but you ▼   reject fail to reject the null​ hypothesis, ▼   Upper H 0 : mu greater than or equals 43H0: μ≥43 Upper H 0 : mu not equals 43H0: μ≠43 Upper H 0 : mu equals 43H0: μ=43 Upper H 0 : mu less than or equals 43H0: μ≤43 Upper H 0 : mu greater than 43H0: μ>43 Upper H 0 : mu less than 43H0: μ<43 .   A type II error will occur if the actual mean of the length of time to play a game is ▼   greater than less than or equal to less than greater than or equal to equal to not equal to 43 ​minutes, but you ▼   fail to reject reject the null​ hypothesis, ▼   Upper H 0 : mu greater than 43H0: μ>43 Upper H 0 : mu equals 43H0: μ=43 Upper H 0 : mu not equals 43H0: μ≠43 Upper H 0 : mu less than or equals 43H0: μ≤43 Upper H 0 : mu less than 43H0: μ<43 Upper H 0 : mu greater than or equals 43H0: μ≥43 .

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 + ...