Question

A study was conducted on the effect of an oral antiplaque rinse on plaque buildup on teeth. Eighteen people whose teeth were thoroughly cleaned and polished were randomly assigned to two groups of nine subjects each. Both groups were assigned to use oral rinses (no brushing) for a two-week period. Group 1, the control group, received a rinse that, unknown to the subjects, contained no antiplaque agent. Group 2 used a rinse that contained an antiplaque agent. A plaque index x, a measure of plaque buildup, was recorded at 4, 7, and 14 days. The mean and standard deviation for the 14-day plaque measurements are shown in the table for the two groups. Control Group Antiplaque Group Sample size Mean Standard deviation 1.22 0.35 0.76 0.35 (a) State the null and alternative hypotheses that should be used to test the effectiveness of the antiplaque oral rinse. HO: (41 - 42) < 0 versus H: (41 - H2) > 0 HO: (41 - 12) = 0 versus H : (41 - H2) 0 HO: (41 - 42) = 0 versus M: (41-42) > 0 HO: (4 - 12) # O versus Hy: (41 - 42) = 0 HO: (44 - ) = 0 versus M: (41-42) <0 (b) Do the data provide sufficient evidence to indicate that the oral antiplaque rinse is effective? Test using a = 0.05. (Round your answers to three decimal places.) Test statistic: t = 2.306 X Rejection region: If the test is one-tailed, enter NONE for the unused region. Conclusion: O Hois rejected. There is insufficient evidence to indicate that the oral antiplaque rise is effective. OH, is not rejected. There is insufficient evidence to indicate that the oral antiplaque rise is effective. O Ho is not rejected. There is sufficient evidence to indicate that the oral antiplaque rise is effective. O Ho is rejected. There is sufficient evidence to indicate that the oral antiplaque rise is effective. (c) Find the approximate p-value for the test. O p-value < 0.005 0.005 <p-value < 0.010 0.010 < p-value < 0.025 0.025 < p-value < 0.050 0.050 < p-value < 0.100 O p-value > 0.100

Answer 1

b)

standard error se=√(S21/n1+S22/n2)=			0.165
test stat t =(x1-x2-Δo)/Se=		2.788

rejection region:

t> 1.746

t<NONE

O Mois rejected. There is sufficient evidence to indicate that the oral antiplaque rise is effective.

0.005 <p-value < 0.010