WARM – UP Plant scientists have developed a new variety of corn rich in amino acid lysine used for bulking up chickens. Twenty-five Chickens were randomly placed in one of two groups (Exclusively eating the New corn & Control group) and after one month their weight gains were recorded (in grams). Control Experimental Corn 380 321 366 356 361 447 401 434 283 349 402 462 403 393 426 406 356 410 329 399 427 420 477 392 430 Is there good evidence that chicks fed high-lysine corn gain more weight?

Control: 367.75 47.165 12 H0: μ1 = μ2 Ha: μ1 < μ2 Experimental: 416.69 28.949 13 μi = The true mean amount of weight gained by chicks eating… μ1 = Traditional Corn μ2 = Experimental Corn H0: μ1 = μ2 Ha: μ1 < μ2 TWO Sample t – Test SRS – Stated 2. Independent 3. Approximately Normal Distribution – Graph BOTH! Since the P-Value is less than α = 0.05 the data IS significant . There is strong evidence to REJECT H0 . Chicks fed the high-lysine corn gained more weight.

Two –Sample T Tests vs. Matched Pairs T Tests Two Sample T – Two INDEPENDENT samples in which no natural pairing exists within the data. Examines the Difference in the Means Matched Pairs T – Two Dependent samples in which a natural pairing does exist within the data. Examines the Mean of the Paired Differences.

Two-Sample vs. Matched Pairs The following data indicates the average age of registered voters before and after the 2004 election. Choose 6 counties. County # Before 04 After 04 1 35 36 2 40 38 3 42 43 4 5 41 37 6 50 49 7 47 8 9 39 10 11 32 1. Design AND Conduct a Two-sample t-Test (both samples n =6) experiment to determine if age significantly decreased. 2. Design AND Conduct a Matched Pairs t-Test (n = 6) experiment to determine if age significantly decreased.

Two-Sample vs. Matched Pairs Randomly Choose 2 samples of 6 counties, 6 B & 6 A. County # Before 04 After 04 1 35 36 2 40 38 3 42 43 4 5 41 37 6 50 49 7 47 8 9 39 10 11 32 1. Design AND Conduct a Two-sample t-Test (n =6) experiment to determine if age significantly decreased. μi= True mean age of voters… i=1 Before 04, i=2 After 04 H0: μ1 = μ2 Ha: μ1 > μ2 TWO Sample t – Test SRS – Stated 2. Independent 3. Approximately Normal Distribution – Graph BOTH! t = ________ P-Value = _______

Two-Sample vs. Matched Pairs Randomly Choose 6 counties. 2. Design AND Conduct a Matched Pairs t-Test (n = 6) experiment to determine if age significantly decreased. County # Before 04 After 04 1 35 36 2 40 38 3 42 43 4 5 41 37 6 50 49 7 47 8 9 39 10 11 32 μd= True mean difference in age of voters. (Before 04, - After 04) H0: μd = 0 Ha: μd > 0 Matched Pairs t – Test SRS – Stated 2. Not Independent 3. Approximately Normal Distribution Graph differences t = ________ P-Value = _______

OBJECTS RECALLED

High cholesterol levels in people can be reduced by exercise, diet, and medication. Twenty middle-aged males with cholesterol readings between 220 and 240 milligrams per deciliter (mg/dL) of blood were randomly selected from the population of such male patients at a large local hospital. Ten of the 20 males were randomly assigned to group A, advised on appropriate exercise and diet, and also received a placebo. The other 10 males were assigned to group B, received the same advice on appropriate exercise and diet, but received a drug intended to reduce cholesterol instead of a placebo. After three months, post-treatment cholesterol readings were taken for all 20 males and compared to pretreatment cholesterol readings. The tables below give the reduction in cholesterol level (pretreatment reading minus post-treatment reading) for each male in the study. Do the data provide convincing evidence, at the α = 0.01 level, that the cholesterol drug is effective in producing a reduction in mean cholesterol level beyond that produced by exercise and diet?