Population: a data set representing the entire entity of interest - What is a population? Sample: a data set representing a portion of a population Population Sample

Population mean – the true mean for that population -a single number Sample mean – the estimated population mean -a range of values (estimate ± 95% confidence interval) Population Sample

As our sample size increases, we sample more and more of the population. Eventually, we will have sampled the entire population and our sample distribution will be the population distribution Increasing sample size

Sample Distribution Approaches Normal Distribution With Sample Size

Variance =  (x-x) 2 N-1  i= x N N Mean = x = Standard Deviation =  (x-x) 2 N-1  Go to Excel Mean = 169/6 = Range = 25 – 32 SOS = Variance = / 5 = 8.16 Std. Dev. =  40.83/5 = 2.86 Std. Err. = 2.86 / √ 6 = 1.17 Standard Error = SD √N

MEAN ± CONFIDENCE INTERVAL When a population is sampled, a mean value is determined and serves as the point-estimate for that population. However, we cannot expect our estimate to be the exact mean value for the population. Instead of relying on a single point-estimate, we estimate a range of values, centered around the point-estimate, that probably includes the true population mean. That range of values is called the confidence interval.

Confidence Interval Confidence Interval: consists of two numbers (high and low) computed from a sample that identifies the range for an interval estimate of a parameter. There is a 5% chance (95% confidence interval) that our interval does not include the true population mean. y ± (t  /0.05 )[(  ) / (  n)] ±    30.45

Hypothesis Testing –Null versus Alternative Hypothesis Briefly: –Null Hypothesis: Two means are not different –Alternative Hypothesis: Two means are not similar A test statistic based on a predetermined probability (usually 0.05) is used to reject or accept the null hypothesis  < 0.05 then there is a significant difference  > 0.05 then there is NO significant difference

Are Two Populations The Same? Boudreaux : ‘My pond is better than your lake, cher’! Alphonse : ‘Mais non! I’ve got much bigger fish in my lake’! How can the truth be determined?

Two Sample t-test Simple comparison of a specific attribute between two populations If the attributes between the two populations are equal, then the difference between the two should be zero This is the underlying principle of a t-test If P-value > 0.05 the means are not significantly different; If P < 0.05 the means are significantly different Go to Excel

Analysis of Variance Can compare two or more means Compares means to determine if the population distributions are not similar Uses means and confidence intervals much like a t-test Test statistic used is called an F statistic (F-test), which is used to get the P value If P-value > 0.05 the means are not significantly different; If P< 0.05 the means are significantly different Post-hoc test separates the non-similar ones Go to SAS