Question

In a study on the effect of an oral rinse on plaque buildup on teeth, fourteen people 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 the rinse contained no antiplaque agent. A measure of plaque buildup was recorded at 14 days with means and standard deviations for the two groups shown in the table.

Control Group   Antiplaque Group

Sample Size                      7                 7

Mean                             1.27             0.75

Standard Deviation     0.34          0.34

(a) State the null and alternative hypotheses that should be used to test the effectiveness of the antiplaque oral rinse.

H0: (μ1 − μ2) = 0 versus Ha: (μ1 − μ2) < 0

H0: (μ1 − μ2) ≠ 0 versus Ha: (μ1 − μ2) = 0   

H0: (μ1 − μ2) = 0 versus Ha: (μ1 − μ2) ≠ 0

H0: (μ1 − μ2) < 0 versus Ha: (μ1 − μ2) > 0

H0: (μ1 − μ2) = 0 versus Ha: (μ1 − μ2) > 0

(b)Do the data provide sufficient evidence to indicate that the oral antiplaque rinse is effective? Test using

α = 0.05.

State the test statistic. (Round your answer to three decimal places.)

t =

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t             >           

t             <           

State the conclusion.

H0 is rejected. There is insufficient evidence to conclude that the oral antiplaque rise is effective.

H0 is not rejected. There is sufficient evidence to conclude that the oral antiplaque rise is effective.   

H0 is not rejected. There is insufficient evidence to conclude that the oral antiplaque rise is effective.

H0 is rejected. There is sufficient evidence to conclude that the oral antiplaque rise is effective.

(c)Find the approximate p-value for the test.

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

p-value > 0.100

Answer 1