Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.5 7.2 7.3 6.3 8.1 6.8 7.0 7.2 6.8 6.5 7.0 6.3 7.9 9.0 8.7 8.7 7.8 9.7 7.4 7.7 9.7 8.0 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.6 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.4 7.3 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.3 Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean μ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean μ2 and standard deviation σ2.   Compute the estimated standard error. (Round your answer to three decimal places.) (c) Calculate a point estimate of the ratio σ1/σ2 of the two standard deviations. (Round your answer to three decimal places.) (d) Suppose a single beam and a single cylinder are randomly selected. Calculate a point estimate of the variance of the difference X − Y between beam strength and cylinder strength. (Round your answer to two decimal places.)

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 + ...