Stat 217
Lab 2

1: Background 2: Descriptive 3: Population Model 4: Simulation 5: Population I 6: Population II 7: Central Limit Theorem 8: Standard Error 9: Theory-based approach 10: Further considerations 11: Conclusions 12: Summary

Central Limit Theorem for Sample Mean

Theoretical Result: If we have either a large sample size (rough guideline: n > 20) OR a normally distributed population, then the sampling distribution of the sample mean is approximately normal or normal with mean equal to (the population mean) and standard deviation equal to / (the population standard deviation divided by the square root of the sample size)

 

This should remind you a lot of the Central Limit Theorem for a sample proportion. The main difference is in the parameter of interest and in the formula for the standard deviation.

Thought Questions

• Is the sample size from our study of Cal Poly sleep times large enough for us to assume that the shape of the distribution of sample means will be approximately normal regardless of the shape of the population? Justify your answer.
• Assuming the null hypothesis (from part (d)) is true, what does the theoretical result predict for the mean of the distribution of sample means?