A sample of size 2 is selected from the following heights of 5 Grade 11 students: Student A: 154 cm Student B: 159 cm Student C: 164 cm Student D: 167 cm Student E: 162 cm Derive the sampling distribution of the sample mean if the sample generated using (a) Simple Random Sample With Replacement (SRSWR); and (b) Simple Random Sample Without Replacement (SRSWOR). Compute the means and standard deviation of the sample means or the standard error under two different sampling schemes.

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A sample of size 2 is selected from the following heights of 5 Grade 11 students:
Student A: 154 cm
Student B: 159 cm
Student C: 164 cm
Student D: 167 cm
Student E: 162 cm
Derive the sampling distribution of the sample mean if the sample generated using
(a) Simple Random Sample With Replacement (SRSWR); and (b) Simple Random
Sample Without Replacement (SRSWOR). Compute the means and standard
deviation of the sample means or the standard error under two different sampling
schemes.
Important formulas to be used:
E(x-u)?
Population Standard deviation: SD =
N
Standard Error (With Replacement): SE
(N-п)
Standard Error (Without Replacement): SE :
vn
(N-1)
Transcribed Image Text:A sample of size 2 is selected from the following heights of 5 Grade 11 students: Student A: 154 cm Student B: 159 cm Student C: 164 cm Student D: 167 cm Student E: 162 cm Derive the sampling distribution of the sample mean if the sample generated using (a) Simple Random Sample With Replacement (SRSWR); and (b) Simple Random Sample Without Replacement (SRSWOR). Compute the means and standard deviation of the sample means or the standard error under two different sampling schemes. Important formulas to be used: E(x-u)? Population Standard deviation: SD = N Standard Error (With Replacement): SE (N-п) Standard Error (Without Replacement): SE : vn (N-1)
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