L7

• The t-distribution is used to test hypotheses about the mean of a population when the sample size is small

  
• The t-distribution models the distribution of sample means when the population standard deviation is unknown

  
• The diagram showing the normal distribution of sample means illustrates that in repeated sampling, 95% of sample means will fall within 1.96 standard deviations of the population mean, and 99% will fall within 2.58 standard deviations

  
• The formula for the confidence interval for a mean is used to compute an interval of values that is almost sure to cover the true population value

  
• Degrees of freedom for hypotheses concerning a single mean are equal to the sample size minus 1, affecting the overall shape of a distribution
• A confidence interval estimate of a parameter consists of an interval of numbers along with a probability that the interval contains the unknown parameter
• 1. test values are used when parameters are not known to compute confidence intervals
• For example, a 95% confidence interval is computed using the sample mean, standard error, and the t value for a specific degree of freedom and probability
• T tests

  the closer t is to 0 the less likely there is a difference between the sample mean and population mean
• Degrees of Freedom

  • a parameter of many statisitcal tests (n-1)