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. (Use ₁ for State 1 and ₂ for State 2.) Sample Size Standard Deviation 100 196 100 163 State State 1 State 2 Mean ܕ ܐ 1,124 1,049 (a) Use the critical value approach to 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. O Ho: (1₂ - 1₂) = 0 versus H₂: (₁H₂) > 0 O Ho: (H₂-H₂) <0 versus H₂: (₁H₂) > 0 Ho: (H₁-H₂) = 0 versus H₂: (H₁-H₂) = 0 O Ho: (H₁-H₂) = 0 versus H₂: (#₁ #₂) <0 O Ho: (H₂-H₂) = 0 versus H₂: (H₁-H₂) = 0 Find the test statistic. (Round your answer to two decimal places.) Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) State your conclusion. O Ho is rejected. There is sufficient evidence to indicate that there is a difference in the average SAT scores for the two states. O Ho is rejected. There is insufficient evidence to indicate that there is a difference in the average SAT scores for the two states. O Ho is not rejected. There is insufficient evidence to indicate that there is a difference in the average SAT scores for the two states. O Ho is not rejected. There is sufficient evidence to indicate that there is a difference in the average SAT scores for the two states. (b) Use the p-value approach to test for a significant difference in the average SAT scores for these two states. (Use a = 0.05.) Find the p-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--- rejected. There is ---Select--- evidence to conclude that (₂-₂) ?~0.

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