Determining The Sample Size (discrete Data) 6cl34

Sample Size Determination for Discrete Data: Before you can calculate a sample size, you need to determine a few things about the target population and the sample you need: 1. Population Size — how many total people fit your demographic? For instance, if you want to know about mothers living in the US, your population size would be the total number of mothers living in the US. Don’t worry if you are unsure about this number. It is common for the population to be unknown or approximated. 2. Margin of Error (Confidence Interval) — No sample will be perfect, so you need to decide how much error to allow. The confidence interval determines how much higher or lower than the population mean you are willing to let your sample mean fall. If you’ve ever seen a political poll on the news, you’ve seen a confidence interval. It will look something like this: “68% of voters said yes to Proposition Z, with a margin of error of +/- 5%.” 3. Confidence Level — How confident do you want to be that the actual mean falls within your confidence interval? The most common confidence intervals are 90% confident, 95% confident, and 99% confident. 4. Proportion – What is your current estimate of the proportion of the population

Sample Size for Discrete Data Formula for determining sample size for discrete data is:

Z is the value from the standard normal distribution reflecting the confidence level that will be used (e.g., Z = 1.96 for 95%)

E is the desired margin of error. p is the proportion of successes in the population

Example 1: An investigator wants to estimate the proportion of freshmen at his University who currently smoke cigarettes (i.e., the prevalence of smoking). How many freshmen should be involved in the study to ensure that a 95% confidence interval estimate of the proportion of freshmen who smoke is within 5% of the true proportion? Because we have no information on the proportion of freshmen who smoke, we use 0.5 to estimate the sample size as follows:

In order to ensure that the 95% confidence interval estimate of the proportion of freshmen who smoke is within 5% of the true proportion, a sample of size 385 is needed.

---------------------------------------------------------------------------------------------Example 2: To estimate the proportion of Malaysian males who smoke, what sample size is required to achieve a 95% confidence interval of width ±5% (that is to be within 5% of the true value)? A study some years ago found that approximately 30% were smokers. Answer P = 0.30, Δ = 0.05 and z = 1.96 n=(1.960.05)20.3(1−0.3)=322.69

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Example 3: In the Al Haouz project in Morocco, it has been estimated that roughly 30% (0.3) of the children in the project area suffer from chronic malnutrition. This figure has been taken from national statistics on malnutrition in rural areas. Use of the standard values listed above provides the following calculation. Answer n=

1.96² x .3(1-.3) .05² n = 3.8416 x .21 .0025 n = .8068 .0025 n = 322.72 ~ 323

To learn about margin of error: http://stattrek.com/estimation/margin-of-error.aspx