Question

1.Using key terms, create a scenario where you can find a population, a sample, the parameter, the statistic, a variable, and data. Post your scenario and provide a detailed description using the key terms. After reviewing the information, what did you learn about your target population?

2.define confidence interval and degree of confidence. provide one example of confidence interval and interpret the result?

Answer 1

Scenario: Suppose you're interested in knowing what percent of all households in a large city have a single women as the head of the household. To estimate this percentage you conduct a survey with 200 household and determine how many of these 200 are headed by a single woman.

Population: A population is the entire group you're are interested in studying.The goal here is to estimate what percent of all households in a large city have a single woman as the head of the household. The population is all households, and the variable is whether a single woman runs the household.

Sample: The sample is a subset drawn from the entire population you're interested in studying. So in this example, the subset is the 200 household selected out of all the households in the city.

Parameter: A parameter is some characteristic of the population. Because the studying the population directly isn't usually possible, parameter are usually estimated by using statistics (number calculated from the sample data) In this example, the parameter is the percent of all households headed by the single woman in the city.

Statistic: The statistic is a number describing some characteristic that you calculate form your sample data; the statistic is used to estimate the parameter (some characteristic in the population) In this example the statistic is the percent of households headed by the single woman among the 200 selected households.

Confidence Interval: A confidence interval gives an estimated  range of values which are likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. (or)

The confidence interval describes the uncertainty associated with a sampling method. Suppose we used the same sample method to select the different samples and to compute different interval estimate for sample. Some interval estimate would include true population parameter and some would not. A 90% of confidence level means that would except 90% of interval estimates include in the population parameter.

Degrees of freedom: Degrees of freedom of an estimate is the number of independent pieces of information that went into calculating the estimate. It's not quite same as the number of items in the sample.

example: Suppose we want to estimate the average weight of adult male in a country. We draw a sample of 1000 population from the population of 1,000,000 men and weight them. We find that average man in our sample weight 180 pounds, and the standard deviation of sample is 30 pounds what is 95% of confidence interval.

1. Identify a sample statistic.: since we are trying to estimate the mean weight in the population, we choose mean weight in our sample(180) as sample statistic.

2.Select a confidence level: In this case we are working with 95% confidence level.

3.Finding the margin of error: Margin of error= critical value* standard error of the statistic

4. Finding the Standard error: The standard error(SE) of the mean is SE=s/square root(n)=30/square root(1000)=0.95

5. The critical value: the critical value is used to compute the margin of error

compute(alpha): alpha= 1-(confidence level/100)=0.05

Find the critical probability(p*)= 1- alpha/2=1-0.05/2=0.975

Find the degrees of freedom=n-1   =1000-1=999

The critical value is the statistic having the degrees of freedom 999 and the cumulative probability equal to 0.975. From t-distribution calculator we find that the critical value is 1.96

Compute the margin error: critical value* Standard error=1.96*0.975=1.86

Specify the confidence interval : The range of confidence interval is defined by the

and the uncertainty denoted by the confidence level. Therefore 95% of confidence interval is