Question

# : Let ?1, ?2,…. . , ?12 (12 random variables iid) like a variable ? (?;...

: Let ?1, ?2,…. . , ?12 (12 random variables iid) like
a variable ? (?; 1). The following data are observed:
2.5345792; 2.5236928; 0.3303505; 0.1267132; 1.3670369; 0.2349068;
1.5209821; 0.6114980; 2.3096728; 1.6590382; 4.0726550; 4.7865432
(1) Give a point estimator of ?.
(2) Find a 99% confidence interval for ?

1. Point estimate of

2. Create the following table.

 data data-mean (data - mean)2 2.5345792 0.6947792 0.48271813675264 2.5236928 0.6838928 0.46770936189184 0.3303505 -1.5094495 2.2784377930503 0.1267132 -1.7130868 2.9346663843342 1.3670369 -0.4727631 0.22350494872161 0.2349068 -1.6048932 2.5756821834062 1.5209821 -0.3188179 0.10164485336041 0.6114980 -1.228302 1.508725803204 2.3096728 0.4698728 0.22078044817984 1.6590382 -0.1807618 0.03267482833924 4.0726550 2.232855 4.985641451025 4.7865432 2.9467432 8.6832954867462

Find the sum of numbers in the last column to get.

So standard deviation is

t value for 99% CI is TINV(0.01,11)=3.106

So Margin of Error is

Hence CI is

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