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Answer A4, B1, and B2:

A. Assume this as your target population. Suppose this data constitute a normal distribution.

1. Find the mean height and the population standard deviation.
2. By simple random sampling, obtain a sample of 10 students. Compute the sample mean. Obtain the 90% confidence interval (CI) of the population mean using this sample.
3. From the sample you obtain in (b), compute the 95% confidence interval of the population mean. What do you observe about the width of 90% CI compared 95% CI. Make a general statement on the margin error as confidence level increases.
4. By simple random sampling, obtain a sample of 20 students. Compute the sample mean. Obtain the 95% CI of the population mean. What do you observe about the width of 95% CI from 20 samples compared to the width of 95% CI from 10 samples. Make a general statement on the margin of error as the sample size increases.

B. Refer to the data about the height 100 senior high school student. Assume this as your target population. Suppose this data constitute a normal distribution.

1. By simple random sampling, obtain a sample of 5 students. Compute the sample mean. Obtain the 90% CI of the population mean using this sample. Repeat this process 20 times. At the end, you will have a list of 20 90%-confidence interval with sample size equal to 5.
2. From 2a, count how many intervals contain the population mean. Is the percent of confidence intervals that contain the population mean μ close to 90%?