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**Subject Mathematics Statistics-R Programming**

Check the file: Questions.pdf

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1.

(a)

I counted how many players in each team in 797 playersâ€™ data using table function, and divide it by 797 to obtain the proportion. I then multiply the proportion by 150 to find the rough estimate of the number of players to be sampled and round them up. The sum of them should be approximately equal to 150. It turns out that all the allocations are 5 and the sum is also exactly 150. Then, I used the 'strata()' function from sampling package to obtain strata samples.

(b)

E(logsal) = 14.5403

C.I. for logsal = [14.37123, 14.70937]

(c)

E(pitcher) = 420.4

C.I. for pitcher = [361.2663, 479.5337]

(d)

The optimal allocation may benefit because it is not clear to say the variances in each strata are even roughly the same....

(a)

I counted how many players in each team in 797 playersâ€™ data using table function, and divide it by 797 to obtain the proportion. I then multiply the proportion by 150 to find the rough estimate of the number of players to be sampled and round them up. The sum of them should be approximately equal to 150. It turns out that all the allocations are 5 and the sum is also exactly 150. Then, I used the 'strata()' function from sampling package to obtain strata samples.

(b)

E(logsal) = 14.5403

C.I. for logsal = [14.37123, 14.70937]

(c)

E(pitcher) = 420.4

C.I. for pitcher = [361.2663, 479.5337]

(d)

The optimal allocation may benefit because it is not clear to say the variances in each strata are even roughly the same....

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