3. James Short (1708–1768), a Scottish optician, constructed the highest-quality reflectors of his time. It was with these reflectors that Short obtained the following measurements of the parallax of the sun (in seconds of a degree), based on the 1761 transit of Venus. The parallax of the sun is the angle a subtended by the Earth, as see from the surface of the sun. Sample Size: n = 53. Mean: ix 8.61. Standard Deviation: s 0.75. 8.50 8.50 7.33 8.64 8.06 8.43 8.44 8.14 8.65 8.35 8.71 8.31 9.71 8.50 8.28 9.87 8.80 8.40 8.82 9.02 10.57 7.99 8.58 8.34 9.64 9.27 9.06 9.25 9.09 8.50 7.68 10.34 8.07 8.36 9.71. 8.36 8.86 8.58 7.80 771 8.30 5.76 8.44 9.11 8.66 8.55 9.54 9.07 8.23 8.50 8.34 8.60 8.34 Source: The data and descriptive information are based on material from Stephen M. Stigler. (1977). Do robust estimators work with real data? Annals of Statistics, 5, 1055-1098. (a) Estimate the 95% upper confidence bound. Be sure to justify your solution both graph- ically and analytically.

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Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.