QUESTION 5 10 points Save Answer We are analyzing the mean of a random variable

Question

QUESTION 5 10 points Save Answer We are analyzing the mean of a random variable X, by looking at a very large random sample (so we use the normal distribution) We found SEOO = 5 , where the sample size is n = 100 The t-statistic is 4, and the null hypothesis was testing What is the sample average X Hint you need first to calculate the standard deviation of the sample average. SEC QUESTION 6 10 points Save Answer We consider the following regression: and the size of the sample we use is n # 87 How many degrees of freedom do we have when analyzing the OLS estimates?

Explanation / Answer

5. S.E (X) = 5

n= 100

t-statistic = 4 and the null hypothesis was H0 : Ux =3

Now, to calculate the sample average( X bar) ,firstly calculate the standard deviation of the sample average ,

S.E(X bar).

We know that t-stastic =( X bar - Ux)/ S.E(X bar) [and t-stastic is given = 4 .]

S.E(X bar) = S.E(X) / root n

= 5 /root 100

= 5/10 = 0.5 = S.E(X bar)

Now, put the value of S.E(X bar) in t-statistic formula ,we get

4 =(( X bar ) - 3) / 0.5

4(0.5) + 3 = X bar

2+ 3 = X bar

X bar i.e sample average = 5

6. n= 87

And there are 4 parameters that are estimating , Therefore,degrees of freedom when anlayzing the OLS estimates = n-4

Degrees of freedom = 87-4 = 83.

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