Quality control of materials is a critical aspect of every civil engineering construction project. During con- struction of a retaining wall for a large wastewater plant in the City of La Serena, you (the consultant) randomly sampled each of six batches of concrete during a certain day's production. Sampling of each batch consisted of several cylindrical concrete specimens. After 28 days, you tested these concrete specimens for their compressive strengths and calculated the average compressive strength (ACS) of each sample. The following results were obtained:
From the contract specifications, the minimum 28-day strength of that grade of concrete is typically 40 N/mm2, which should be attained before the concrete is accepted.
(a) Provide a simple plot of the mean strength of various samples.
(b) From your sketch in (a), describe qualitatively the bias and efficiency of the estimate of the population mean.
(c) Compute the estimated mean of the population (calculated as the mean of the sample means). Is your estimated population mean biased from the true population mean?
(c) Assess the efficiency of the estimate by computing the variance of the sample means.