You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02.       Ho:μ1=μ2Ho:μ1=μ2       Ha:μ1<μ2Ha:μ1<μ2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain the following two samples of data. Sample #1 Sample #2 61.5 80.2 53.7 61.5 73.7 82.6 76.7 96.3 50 60.5 74.9 85.8 88.7 90.3 63.4 93.5 71.1 94 83 66.9 83 72.9 74.5 85.8 71.5 99.7 94.9 92.4 86 93.7 78.8 99.7 91.2 96 82.7 88.6 91 89.8 90 92.7 98.3 98 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =  What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.) p-value =  The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean. There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean. The sample data support the claim that the first population mean is less than the second population mean. There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.

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 + ...