In a study on the effect of an oral rinse on plaque buildup on teeth,eighteenpeople whose teeth were thoroughly cleaned and polished were randomly assigned to two groups ofninesubjects each. Both groups were assigned to use oral rinses (no brushing) for a2-weekperiod.Group 1used 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 at14 dayswith means and standard deviations for the two groups shown in the table.

Control GroupAntiplaque GroupSample Size99Mean1.210.75Standard Deviation0.350.35

(a)

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

H₀: (₁₂) = 0 versusH_a: (₁₂) < 0

H₀: (₁₂) = 0 versusH_a: (₁₂) > 0

H₀: (₁₂) = 0 versusH_a: (₁₂)0

H₀: (₁₂) < 0 versusH_a: (₁₂) > 0

H₀: (₁₂)0 versusH_a: (₁₂) = 0

(b)

Do the data provide sufficient evidence to indicate that the oral antiplaque rinse is effective? Test using= 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.

H₀is not rejected. There is sufficient evidence to conclude that the oral antiplaque rise is effective.

H₀is rejected. There is insufficient evidence to conclude that the oral antiplaque rise is effective.

H₀is not rejected. There is insufficient evidence to conclude that the oral antiplaque rise is effective.

H₀is rejected. There is sufficient evidence to conclude that the oral antiplaque rise is effective.

(c)

Find the approximatep-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

You may need to use the appropriateappendix tableto answer this question.