business stat exam help

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Chapter 11

• Interval Estimation of a Population Variance

𝑛 − 1 𝑠!

𝜒! !

! ≤ 𝜎 ! ≤

𝑛 − 1 𝑠!

𝜒 !!!!

!

where 𝜒! values are based on a chi-squared distribution with (n-1) degrees of freedom.

• Hypothesis Testing about the Variances of Two Populations

Test Statistic

𝑭 = 𝒔𝟏𝟐

𝒔𝟐𝟐

The critical value 𝐹! is based on an F distribution with 𝑛! − 1 (numerator) and 𝑛! − 1 (denominator) degrees of freedom

Chapter 13

Test for the Equality of k Population Means

𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑠 = 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑠

𝑑𝑒𝑔𝑟𝑒𝑒𝑠 𝑜𝑓 𝑓𝑟𝑒𝑒𝑑𝑜𝑚 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡

𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝐸𝑟𝑟𝑜𝑟 = 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒 𝐸𝑟𝑟𝑜𝑟

𝑑𝑒𝑔𝑟𝑒𝑒𝑠 𝑜𝑓 𝑓𝑟𝑒𝑒𝑑𝑜𝑚 𝐸𝑟𝑟𝑜𝑟

𝐹 = 𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑠

𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝐸𝑟𝑟𝑜𝑟

The critical value 𝐹!is based on an F distribution with k-1 numerator degrees of freedom and n-k denominator degrees of freedom.

Chapter 14 (Simple Linear Regression) b 1 =

!!! ! (!!! !) !!! ! ²

b1: slope coefficient in a simple regression line b0: intercept coefficient (coefficient of the constant) in a simple regression line 𝑦: estimated value of the dependent variable y

b0 = 𝑦 − b!x 𝑦 = b0 + b 1 x (estimated equation)

2

𝑆𝑆𝐸 = (𝑌! − 𝑌)² SST = SSR + SSE ⟹

(𝑌! − 𝑌)² = SST = ( 𝑌 −𝑌)²+ (𝑌! − 𝑌)²

𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑒𝑥𝑝𝑙𝑎𝑖𝑛𝑒𝑑 𝑏𝑦 𝑟𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 = 𝑆𝑆𝑅 = ( 𝑌 −𝑌)² total variation in Y = SST = (𝑌! − 𝑌)² R2 = !!"

!!" =coefficient of determination,

sample correlation coefficient = 𝑟!,! = 𝑅² (carry the sign of b1) tstat = b1 / se(b1), se(b1):standard error of the slope coefficient, residual = error = Y-𝑌