Question

At the end of every school year, the state administers a reading test to a simple random sample drawn without replacement from a population of 20,000 third graders. This year, the test was administered to 8 students selected via simple random sampling. The test score from each sampled student is shown below:

50, 55, 60, 62, 62, 65, 67, 67
Using sample data, estimate the mean reading achievement level in the population.

1. Find the margin of error and the confidence interval. Assume a 95% confidence level.
2. Calculate (a) population mean Y , and (b) population variance σ2
3. Enumerate all possible SRS WR samples of size n =2. Obtain sampling distribution of mean, and hence show that

a) Ey=Y=μ      ?) Vy=σ2n        ?) Es2=σ2

4. Enumerate all possible SRS WOR samples of size n =2. Obtain sampling distribution of mean, and hence show that

a) Ey=Y=μ      ?) Vy=N-nNnσ2        ?) Es2=S2

5. Find 95% confidence interval for the total if selection (1) WR and (2) WOR for all possible samples of size n =2.

Answer 1