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### STAT 330: 96-3

Assignment 1

1. An experiment was carried out to determine the effect of providing free milk to school children in a certain school district. Some children in each school were chosen for the treatment group and got free milk; others were chosen as controls and got no milk. Assignment to treatment or control was done at random. It was feared that assignment in this manner might lead, by chance, to small differences in background between the two groups. Teachers were therefore permitted to use their judgement to switch a few students to balance the groups more effectively. Identify the bias which may have been introduced and say what the likely effect of the bias might be expected to be. You must use common sense to answer this question.

2. A manufacturer sells 500 gram packages of coffee. Federal inspectors select 64 packages at random from a month's production. The selected packages have an average weight of 498.5 grams. The manufacturers defend themselves against a charge of short weight by saying that some variation in packed weight is inevitable. They say they use a machine which puts in an average of 500 grams with a standard deviation of 4 grams and that it was just bad luck that the 64 sampled packages had such a low average weight. Is the manufacturers claim credible?

3. The concentration of cadmium in a lake is measured 17 times. The measurements average 211 parts per billion with an SD of 15 parts per billion. Could the real concentration of cadmium be below the standard of 200 ppb?.

From Devore p 283 (265 in 3rd ed.) #4, 6, p 290 (p 271) #16, 18. p 314 (p 294) # 10. These exercises are review of Stat 270 material.

DUE: Monday, 16 September

Solutions