Managers at an automobile manufacturing plant would like to examine the mean completion time,  μ , of an assembly line operation. The past data indicate that the mean completion time is  42  minutes, but the managers have reason to believe that this value has increased. The managers plan to perform a statistical test. After choosing a random sample of assembly line completion times, the managers compute the sample mean completion time to be  43  minutes. The standard deviation of the population of completion times can be assumed not to have changed from the previously reported value of  4  minutes.   Based on this information, answer the questions below. What are the null hypothesis ( H0 ) and the alternative hypothesis ( H1 ) that should be used for the test? H0 :  μ  is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?42443 H1 :  μ  is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?42443 In the context of this test, what is a Type I error? A Type I error is ?rejectingfailing to reject the hypothesis that  μ  is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?42443 when, in fact,  μ  is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?42443. Suppose that the managers decide not to reject the null hypothesis. What sort of error might they be making? ?Type IType II

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 + ...