Informal Confidence Intervals Pop A Pop B Is

Informal Confidence Intervals Pop A Pop B Is there a difference?

Making an Inference For an inference to be made in determining whethere is a difference between the population medians of two groups, an estimate must be made for each of the population medians. Every sample median provides an estimate of the population median. Every sample taken will have a different median (sampling variability), therefore an interval estimate for the population median is created.

Informal Confidence Intervals This interval is known as an informal Confidence Interval. Different samples will give different informal Confidence Intervals for the population median. Approximately 90% of the intervals will contain the actual population median. This means that it is a fairly safe bet (I am confident), that the population median lies inside the confidence interval.

Calculation of Informal Confidence Intervals The interval created by this process is called an informal confidence interval for the population median.

Calculation of Informal Confidence Intervals

Displaying the confidence interval on box plots It is shown on the box plot by a clear defined horizontal line extending from the median Note that the line is symmetrical (same length) either side of the median.

Informal Confidence Intervals for comparable groups Male: [27, 37] Female: [29, 44] NOTE: Discussion of what each informal confidence interval means (in context & referring back to the population, and how sure you are) Males: From the informal confidence interval, I am reasonably confident that the population median number of hours worked for males is between 27 and 37 hours of work per week. Females: From the informal confidence interval, I am reasonably confident that the population median number of hours worked for females is between 29 and 44 hours of work per week.

Statistical Inference – making a decision How can we use the confidence intervals to help make a decision on whethere is a difference between the two population medians to draw a conclusion? Is there an overlap between the informal confidence intervals? How does Population A compare to Population B?

Informal Confidence Intervals – no overlap As the informal confidence intervals do not overlap, it is therefore unlikely that the populations have equal medians. There is sufficient evidence to make the claim that the median number of beach crossings made in spring/summer tends to be greater than the median number of beach crossings made in winter.

Informal Confidence Intervals – overlap As the informal confidence intervals overlap, it cannot be said that the medians are likely to be different back in the population. There is insufficient evidence to make the claim that the median number of beach crossings made in spring/summer tends to be greater than the median number of beach crossings made in winter.

Statistical Inference You must make an inference, which will be a conclusion about the population medians based on their samples taken from the population. Your conclusion will answer the posed investigative question and will involve making a call about the population medians. The informal confidence intervals will be used to make an inference about the population medians.

Summing Up • Due to sampling variability, different samples will give different informal confidence intervals for the population median • However, about 90% of the intervals constructed in this way will contain the actual value of the population median • This means that it is a fairly safe bet that the population median lies inside the confidence interval