Question

Describe examples of situations where you could appropriately use the following. Explain why the procedure is the correct one to use and identify the statistic to be used and explain why that is the correct choice. (1 point each)

1. Confidence interval for a proportion.
2. Confidence interval for a mean, unknown σ.
3. Confidence interval for a mean, σ known.

Describe procedure for following and provide an example of the calculations:

4. Margin of error calculation for 95% confidence level.
5. Sample size determination for 95% confidence level.

Answer 1

Answer:

a)

If we wish to estimate the proportion of people with diabetes in a population, we consider a diagnosis of diabetes as a "success" (i.e an individual who has the outcome of interest), and we consider lack of diagnosis of diabetes as a "failure." In this example, X represents the number of people with a diagnosis of diabetes in the sample. The sample proportion is p̂ (called "p-hat"), and it is computed by taking the ratio of the number of successes in the sample to the sample size, that is:

The formula shown in the above example for a CI for p is used under the condition that the sample size is large enough for the Central Limit Theorem to be applied and allow you to use a z*-value, which happens in cases when you are estimating proportions based on large-scale surveys.

b)

In most practical research, the standard deviation for the population of interest is not known. In this case, the standard deviation is replaced by the estimated standard deviation s, also known as the standard error. Since the standard error is an estimate for the true value of the standard deviation, the distribution of the sample mean is no longer normal with mean and standard deviation . Instead, the sample mean follows the t distribution with mean and standard deviation . The tdistribution is also described by its degrees of freedom. For a sample of size n, the t distribution will haven-1 degrees of freedom

c) For a population with unknown mean and known standard deviation , a confidence interval for the population mean, based on a simple random sample (SRS) of size n, is

d)

A margin of error tells you how many percentage points your results will differ from the real population value. For example, a 95% confidence interval with a 4 per cent margin of error means that your statistic will be within 4 percentage points of the real population value 95% of the time.

The Margin of Error can be calculated in two ways:

1. The margin of error = Critical value x Standard deviation
2. The margin of error = Critical value x Standard error of the statistic

THANK YOU!