omework: Chapter 5 Homework Save core: 0 of 1 pt xercise 5.8 Suppose that (Y X 1

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omework: Chapter 5 Homework Save core: 0 of 1 pt xercise 5.8 Suppose that (Y X 10f 9 (7 complete) Hw Score: 60.37%, 5.43 of 9 pts -Question Help * satisfy the assumptions specified here and in addition,isn(od and independent of X Arardom sample of n-27isdrawn and yields ys 42.54 + 71.34X, R = 0.54, SER = 1.2 (9.5) (6.8) Where the numbers in parentheses are the homoskedastic-only standard errors for the regression coefficients Po andp respectively. Refer to the student distribution with n-2 degrees of freedom to answer the following questions. Construct a 95% confidence interval for 0 using the student t distribution (with n-2 degrees of freedom) table available here The 95% confidence interval for ° is [OD (Round your responses to two decimal places) nter your answer in the edit fields and then click Check Answer

Explanation / Answer

Consider the given problem, here we need to find out the 95% C.I. for “b0”.

So, here the estimated value of “b0=42.54” and the SE(b0)=9.5” with sample size n=27.

Here the a=5%, the level of significance, => a/2=2.5%, and the 2 critical point be “t(2.5, 25)=2.06”

and “t(-2.5, 25) = - t(2.5, 25) = - 2.06”

So, the C.I. is given by,

=> "(-2.06) <= (42.54 – b0) / 9.5 <= 2.06", => "(-2.06*9.5) <= (42.54 – b0) <= 2.06*9.5",

=> "(-19.57 – 42.54) <= (– b0) <= 19.57 – 42.54",

=> "(-62.11) <= (– b0) <= – 22.97", => "22.97 <= b0 <= 62.11",

=> "22.97 <= b0 <= 62.11".

So, the lower limit be "22.97" and the uper limit be "62.11".

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