Hey guys, I recently held a poll in this forum to find out what people are struggling with most, and it seemed that a lot of people are having trouble with the new study design topic. I've decided to write a quick guide with some example questions for you below

**Sample Statistics:****Example:** In a recent survey, 1 in 5 students indicated that they ate potato crisps or other salty snacks at least four times per week. Is this a sample statistic or a population parameter?

**Answer:** This is a sample statistic. Why?

A

sample statistic gives an estimated statistic based on a sample from a population. A

population parameter gives a true statistic of a whole population.

Eg. With the above question, it is highly unlikely that the survey asked all students in Australia (or whatever the population is) if they eat potato crisps. Therefore, this estimated statistic is representative of the whole population as part of a sample, because the survey was conducted with a portion of the population

**Distribution of p****Example:** 10. In a particular country town, the proportion of employment in the farming industry is 0.62. Five people aged 15 years and older are selected at random from the town.

a. What are the possible values of the sample proportion, p^, of workers in the farming industry?

b. Use this information to construct a probability distribution table to represent the sampling distribution of the sample proportion of workers in the farming industry.

c. Find the probability that the proportion of workers in the farming industry in the sample is greater than 0.5.

**Answer:****Confidence Intervals/Margin of Error****Example:** Tatiana is conducting a survey to estimate the proportion of Year 12 students who will take a gap year after they complete their VCE. Previous surveys have shown the proportion to be approximately 15%. Determine the required size of the sample so that the margin of error for the survey is 3% in a confidence interval of approximately 95% for this proportion.

**Answer:****Confidence interval:** A confidence interval is the proportion of data that lies in the middle of the graph. This means that if you have a confidence interval of 95%, 95% of data is in the middle, which leaves 2.5% on each side. If you have a 99% confidence interval, this leaves 0.5% of data on each side.**How to work out z-score:****Margin of error:** A margin of error is very difficult to define. It is explained in textbooks as “The distance between the endpoints of the confidence interval and the sample estimate”. It’s a bit ambiguous what this means, but you don’t really need to understand it. All you need to know is this:where M = margin of error

z = z-score of confidence interval (use above working to figure this out)

p = sample proportion

n = sample size

Good luck guys and I hope this helps! Let me know if you have any questions