Chapter 14
Supplemental Instruction
Iowa State University / Leader: / Carly
Course: / Stat 226
Instructor: / (Various)
Date: / 3/6/13
Agenda:
Opening Activity: Last-Minute Homework Questions
Die Rolling Activity
Closing Activity: Self Quiz
Die Rolling Activity:
Let X be a random variable representing the roll of a fair 6-sided die. Complete the following table which will represent the theoretical distribution of X (Value of the Die and its corresponding probability).
Table 1:
Die Value (x) / Probability that X = x1
2
3
4
5
6
Exercise Questions:
Recall the premise of the Central Limit Theorem: the mean of a random sample (X) will approximately follow a normal distribution with mean μ and standard error σn, regardless of the distribution of the population (X). The theory requires a sample size of at least 30 if the population distribution is unknown.
1.) Label the histograms on the previous page for n = {2, 10, 30}.
2.) Comment on the difference in shape between each of the histograms, including the population distribution.
3.) How does the CLT come into play here?
4.) If the population has a standard deviation of σ and the mean of a sample distribution has a standard error of σn , which one of these two values will be lower if n>1? Hence, which one of these two distributions do you expect to have lower variability: the population distribution or sampling distribution?
5.) Looking at the each histogram, which one appears to have the least variance?
Self Quiz:
1.) The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normal if…
- All possible samples are selected
- The sample size is large
- The standard error of the sampling distribution is small
2.) The Central Limit Theorem says that the mean of the sampling distribution of the sample means is…
- Equal to the population mean divided by the square root of the sample size
- Close to the population mean if the sample size is large
- Exactly equal to the population mean
3.) The Central Limit Theorem says that the standard deviation of the sampling distribution of the sample mean is…
- Equal to the population standard deviation divided by the square root of the sample size
- Close to the population standard deviation if the sample size is large
- Exactly equal to the standard deviation of the population distribution
4.) Samples of size 25 are selected from a population with mean 40 and standard deviation 7.5. The mean of the sampling distribution of sample means is…
- 7.5
- 8
- 40
5.) Samples of size 25 are selected from a population with mean 40 and standard deviation 7.5. The standard error of the sampling distribution of sample means is…
- 0.3
- 1.5
- 7.5