Statistics 101 Class 9

Overview Last class Last class Our FAVORATE 3 distributions Our FAVORATE 3 distributions The one sample Z-test The one sample Z-test The one sample t-test The one sample t-test A t-test table A t-test table Point estimates and confidence intervals Point estimates and confidence intervals Summary Summary

Last Class We examined how we would determine whether or not to reject the null hypothesis (determine whether or not it is likely that our sample came from the same or a different distribution) when we We examined how we would determine whether or not to reject the null hypothesis (determine whether or not it is likely that our sample came from the same or a different distribution) when we –KNEW the population mean and SD –We had ONLY one observation in our sample NOW we look at what we do when we have more than one observation in our sample NOW we look at what we do when we have more than one observation in our sample

Comparison of Three Types of Distributions

Hypothesis Testing With a Distribution of Means - I Case for when we KNOW the POPULATION distribution mean and standard deviation Case for when we KNOW the POPULATION distribution mean and standard deviation We use this information to estimate the sampling distribution information We use this information to estimate the sampling distribution information It is the comparison distribution when a sample has more than one individual It is the comparison distribution when a sample has more than one individual Find a Z score of your sample’s mean on a distribution of means Find a Z score of your sample’s mean on a distribution of means

Z Test for a Single Sample Cutoff sample score for rejecting the null hypothesis Cutoff sample score for rejecting the null hypothesis –Z table Sample mean’s score on the comparison distribution Sample mean’s score on the comparison distribution –Z score

Hypothesis Testing With a Distribution of Means - II Case for when we KNOW the POPULATION distribution mean BUT NOT the standard deviation Case for when we KNOW the POPULATION distribution mean BUT NOT the standard deviation Since we do not know the standard deviation for the POPULATION to calculate the standard error (SD of the sampling distribution) we use the NEXT BEST THING – the standard deviation from the sample we collected. Since we do not know the standard deviation for the POPULATION to calculate the standard error (SD of the sampling distribution) we use the NEXT BEST THING – the standard deviation from the sample we collected. We use this information to estimate the sampling distribution information We use this information to estimate the sampling distribution information It is the comparison distribution when a sample has more than one individual It is the comparison distribution when a sample has more than one individual Find a t-score of your sample’s mean on a distribution of means Find a t-score of your sample’s mean on a distribution of means

t Test for a Single Sample Cutoff sample score for rejecting the null hypothesis Cutoff sample score for rejecting the null hypothesis –t table Sample mean’s score on the comparison distribution Sample mean’s score on the comparison distribution –t score You also need to know the number of pieces of information that you have. This is called the degrees of freedom (df). For this test the df =n-1 You also need to know the number of pieces of information that you have. This is called the degrees of freedom (df). For this test the df =n-1

T- table

Estimation, Standard Errors, and Confidence Intervals Estimating the mean: point estimates Estimating the mean: point estimates Accuracy of a point estimate Accuracy of a point estimate Interval estimates Interval estimates –Confidence limits –95% confidence interval –99% confidence interval

Estimation, Standard Errors, and Confidence Intervals Steps for figuring confidence limits Steps for figuring confidence limits 1. Figure the standard error 2. Figure the raw scores for 1.96 standard errors (95% confidence interval) or 2.57 standard errors (99% confidence interval) above and below the sample mean

Summary Last class Last class Our FAVORATE 3 distributions Our FAVORATE 3 distributions The one sample Z-test The one sample Z-test The one sample t-test The one sample t-test A t-test table A t-test table Point estimates and confidence intervals Point estimates and confidence intervals