STAT 200 QUIZ 3 | Complete Solution

STAT 200 QUIZ 3 | Complete Solution

Parameter - is a number that describes some aspect of a population

Statistic - is a number that is computed from the data in a sample

Statistical Inference - is the process of drawing conclusions about the entire population based on the information in a sample

Best Estimate - If we only have one sample and we don't know the value of the population parameter, the sample statistic is our best estimate of the true value fo the population parameter

Sampling Distribution - is the distribution of sample statistics computed for different samples of the same size from the same population. A sampling distribution shows us how the sample statistic varies from sample to sample

Shape and Center of a Sampling Distribution - For most of the parameters we consider, if samples are randomly selected and the sample size is large enough, the sampling distribution will be symmetric and bell-shaped and centered at the value of the population parameter

Standard Error - the standard error of a statistic, denoted SE, is the standard deviation of the sample statistic

Sample Size Matters - As the sample size increases, the variability of sample statistics tends to decrease and sample statistics tend to be closer to the true value of the population parameter

Inference Caution - Statistical inference is built on the assumption that samples are drawn randomly from a population. Collecting the sample data in a way that biases the results can lead to false conclusions about the population

Using a margin of error to give a range of plausible values - Recall that the best estimate for a population parameter is the relevant sample statistic. We can expand this idea to give a range of plausible values for the population parameter using: Sample statistic +- margin of error. Where the margin of error is a number that reflects the precision of the sample statistic as an estimate for this parameter.

Confidence Interval - A confidence interval for a parameter is an interval computed from sample data by a method that will capture the parameter for a specificed proportion of all samples. 

The success rate (proportion of all samples whose intervals contain the parameter) is known as the confidence level.

95% Confidence Interval using the Standard Error - If we can estimate the standard error SE and if the sampling distribution is relatively symmetric and bell-shaped, a 95% confidence interval can be estimated using: Statistic +- 2 * SE

Margin of error - the amount added and subtracted in a confidence interval

Standard error - is the standard deviation of the sample statistics if we could take many samples of the same size

Standard Deviation - standard deviation of a sample is the standard deviation of the individual values in that one sample

Interpreting Confidence Level - The confidence level indicates how sure we are that our interval contains the population parameter. for example, we interpret a 95% confidence level by saying we are 95% sure that the interval contains the population parameter

Misinterpretation 1 - A 95% confidence interval contains 95% of the data in the population.

This is a common mistake! The 95% confidence interval for the mean BMI of US adults computed goes from 27.637 to 27.673. It certainly isn't true that 95% of all adults living the US have a BMI within the narrow range. Remember that the confidence interval is built to try and capture a parameter of the population, not individual cases. The correct statement is that we are 95% confident that the population mean is in the interval.

Misinterpretation 2 - I am 95% sure that the mean of a sample will fall within a 95% confidence interval for the mean. 

The correct statement is that we are 95% sure that the mean of the population will fall within a 95% confidence interval for the mean. In fact we are 100% sure that the mean of our sample falls within the confidence interval since we constructed the confidence interval around the sample mean. A confidence interval gives us information about the population parameter, n