Use the information provided to answer the questions.

Population12Sample Size1514Sample Mean34.732.3Sample Variance4.45.8

State the null and alternative hypotheses for testing for a significant difference in means.

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

Calculate the pooled estimate of²,

the associated degrees of freedom, and the observed value of thetstatistic. (Rounds²and yourtstatistic to three decimal places.)

s²=df=t=

What is the rejection region using= 0.05?

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

t>t<

What can be said about thep-value for the test?

p-value < 0.010

0.010 <p-value < 0.020

0.020 <p-value < 0.050

0.050 <p-value < 0.100

0.100 <p-value < 0.200

p-value > 0.200

What can you conclude from these data?

H₀is not rejected. There is sufficient evidence to conclude that there is a significant difference between the population means.

H₀is rejected. There is insufficient evidence to conclude that there is a significant difference between the population means.

H₀is not rejected. There is insufficient evidence to conclude that there is a significant difference between the population means.

H₀is rejected. There is sufficient evidence to conclude that there is a significant difference between the population means.

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