James Short was a maker of optical instruments, particularlytelescopes. He was born in Edinburgh, Scotland and entered theUniversity of Edinburgh in 1726, where he attended lectures by themathematician Colin Maclaurin. Short is perhaps best remembered forhis observations of the transit of Venus on June 6, 1761. Hisprofession made him quite a rich man, by the way. The attachedtable (see the txt file) provides James Short's measurements of theparallax of the sun (in seconds of a degree), based on the 1761transit of Venus. There were two samples of observations collected(under two different conditions). The total number of cases is 53and the "true" value is 8.798. The parallax of the sun is the anglesubtended by the earth, as seen from the surface of the sun.
a) Construct the 95% confidence interval for ? based on thecombined sample. Is the true value of the parallax of the sun inthis interval?
b) Construct the 95% confidence interval for ? based on thecombined sample.
c) Test a hypothesis that the parallax of the sun differs from 9seconds of a degree, based on the combined sample at the 0.1significance level.
d) For two samples, verify if the true means of the populationsthey are taken from differ insignificantly at the 0.05 significancelevel.
e) For two samples, verify if the ratio of the true variances ofthe populations they are taken from differ insignificantly at the0.05 significance level.
f) Write a short summary of your analysis. Show your work. Writeclearly all assumptions.
txt file is below,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,ParallaxSample 18.58.57.338.649.279.069.259.098.58.068.438.448.147.6810.348.07Sample 28.369.718.658.358.718.318.368.587.87.718.39.718.58.289.878.865.768.448.238.58.88.48.829.0210.579.118.668.348.67.998.588.349.648.348.559.549.07
