Jan Lindhe conducted a study16 on the effect of an oral antiplaque rinse on plaque buildup on teeth. Fourteen subjects, whose teeth were thoroughly cleaned and polished, were randomly assigned to two groups of seven subjects each. Both groups were assigned to use oral rinses (no brushing) for a 2-week period. Group 1 used a rinse that contained an antiplaque agent. Group 2, the control group, received a similar rinse except that, unknown to the subjects, the rinse contained no antiplaque agent. A plaque index y, a measure of plaque buildup, was recorded at 4, 7, and 14 days. The mean and standard deviation for the 14-day plaque measurements for the two groups are given in the following table: Control Group Antiplaque Group Sample size 7 7 Mean 1.26 .78 Standard deviation .32 .32 a State the null and alternative hypotheses that should be used to test the effectiveness of the antiplaque oral rinse. b Do the data provide sufficient evidence to indicate that the oral antiplaque rinse is effective? Test using = .05. c Bound or find the p-value for the test.
Week Three Lecture #1: Statistical inference: We infer conclusions about the population with data collected from a subgroup of selected individuals Inference: The value of the statistic changes with the sample sample variability We end up with sampling distribution of the values taken by the statistic in all possible samples of the same size from the same population This distribution is characterized by its center and the spread Center of Distribution: Center of distribution= mean value of the statistic It is related to the bias of the statistic To avoid bias we need randomized samples 2 principle of Experimental design (Randomize) How does randomizing affect the statistic and its distribution Unbiased estimat
