Consider the pooled t variable T which has a t distribution with m n 2 df when both population distributions are normal with 1 2 (see the Pooled t Procedures subsection for a description of Sp). a. Use this t variable to obtain a pooled t confidence interval formula for 1 2. b. A sample of ultrasonic humidifiers of one particular brand was selected for which the observations on maximum output of moisture (oz) in a controlled chamber were 14.0, 14.3, 12.2, and 15.1. A sample of the second brand gave output values 12.1, 13.6, 11.9, and 11.2 (Multiple Comparisons of Means Using Simultaneous Confidence Intervals, J. of Quality Technology, 1989: 232241). Use the pooled t formula from part (a) to estimate the difference between true average outputs for the two brands with a 95% confidence interval. c. Estimate the difference between the two s using the two-sample t interval discussed in this section, and compare it to the interval of part (b). 35.

Week 8: Normal Distribution 25 October 2016 Basic Statistics for Research Professor HK Dong Wendy Liu Probability density function f(x) – describes the distribution of probability for the continuous random variable. It has the properties The total area under the probability density curve is 1 area under the probability density curve between a and b for all x Normal distribution – bell-shaped density curve Mean = µ Standard deviation = σ Normal distribution w/ mean of µ and st. dev of σ is denoted by N(µ, σ) Standard normal distribution: N(0,1) Groundwork for Inferential Statistics Sampling distribution of a statistic o distribution of all possible observations of the statistic for samples of