Question

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

5.8	7.2	7.3	6.3	8.1	6.8	7.0	7.4	6.8	6.5	7.0	6.3	7.9	9.0
8.4	8.7	7.8	9.7	7.4	7.7	9.7	8.1	7.7	11.6	11.3	11.8	10.7

The data below give accompanying strength observations for cylinders.

6.8	5.8	7.8	7.1	7.2	9.2	6.6	8.3	7.0	8.5
7.5	8.1	7.4	8.5	8.9	9.8	9.7	14.1	12.6	11.8

Prior to obtaining data, denote the beam strengths by X₁, . . . , X_m and the cylinder strengths by Y₁, . . . , Y_n. Suppose that the X_i's constitute a random sample from a distribution with mean μ₁ and standard deviation σ₁ and that the Y_i's form a random sample (independent of the X_i's) from another distribution with mean μ₂ and standard deviation σ₂.

1)Compute the estimated standard error. (Round your answer to three decimal places.)

2)Calculate a point estimate of the ratio σ₁/σ₂ of the two standard deviations. (Round your answer to three decimal places.)

3)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.)

Answer 1