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null and alternative hypothesis



Problem 3: Assume that ‘nature‘ behaves according to the fiollowing linear additive model:
1’ = Ho + .3137 + a, where e is a Gaussian random variable .N' (0,03). Using this model, nature generates the following training dataset: 5
D = {(93, yi)}5_1 = {(—23 _7/2) I (—11 _3)){030)t(133)1(21 1(2)} '
Please, answer the questions below without the help of any computer software:
a. Compute the estimates of 30 and B; for a linear estimator F = 30 + fiIX using the data in D. b. Compute the BBB, BBB, T53 and 32 of the linear fit. e. Compute the 95% confidence intervals for flu and £1. (Hint: You can use the RSE as an estimate of
the standard deviation of e). :1. Can you reject the null hypothesis Hg : 161 = 0?

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