How do states stack up against each other in SAT scores? To compare State 1 and State 2 scores, random samples of 100 students from each state were selected and their SAT scores recorded with the following results. (Use₁for State 1 and₂for State 2.)

StateMeanSample

SizeStandard

DeviationState 11,121100192State 21,047100167(a)

Use thecritical value approachto test for a significant difference in the average SAT scores for these two states at the 5% level of significance.

State the null and alternative hypotheses.

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

Find the test statistic. (Round your answer to two decimal places.)

z=

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

z>z<

State your conclusion.

H₀is rejected. There is insufficient evidence to indicate that there is a difference in the average SAT scores for the two states.

H₀is not rejected. There is insufficient evidence to indicate that there is a difference in the average SAT scores for the two states.

H₀is not rejected. There is sufficient evidence to indicate that there is a difference in the average SAT scores for the two states.

H₀is rejected. There is sufficient evidence to indicate that there is a difference in the average SAT scores for the two states.

(b)

Use thep-value approachto test for a significant difference in the average SAT scores for these two states. (Use= 0.05.)

Find thep-value. (Round your answer to four decimal places.)

p-value =

If you were writing a research report, how would you report your results?

The null hypothesis

---Select---

is not

is

rejected. There is

---Select---

insufficient

sufficient

evidence to conclude that(₁₂)

?

<

=

>

0.

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