Final answer:
The-student's-questions-concern-statistical-tests-like-hypothesis-tests-and-correlation-tests-for-data-analysis,-with-specific-contexts-such-as-political-science-biology,-and-probability-analysis.
Step-by-step explanation:
The-series-of-questions-posed-by-the-student-deal-with-various-statistical-tests-used-to-analyze-data-and-infer-conclusions-in-contexts-such-as-political-science,-biology,-and-probability,
-For-example,-to-determine-if-Democratic-senators-are-older-than-Republican-senators,on-average,-one-would-perform-a-hypothesis-test-using-the-stipulated-5-percent-significance-level.-The-student-is-guided-to-consider-whether-the-population-standard-deviations-are-known,-which-dictates-the-test-to-be-used-(-possibly-a-t-test-or-a-z-test-).
-In-a-scenario-investigating-a-relationship-between-population-size-and-homicide-rate,a-correlation-test-such-as-Pearson's-r-may-be-applied-to-determine-if-a-linear-relationship-is-present,-again-using-a-0.05-significance-level-to-assess-the-strength-of-evidence.
-The-student-is-also-queried-about-the-direction-of-hypothesis-tests;-a-not-equals-symbol-in-the-alternative-hypothesis-prompt-the-use-of-a-two-tailed-test,-whereas-a-greater-than-or-less-than-symbol-would-indicate-a-one-tailed-test.-Additionally,-the-nature-of-goodness-of-fit-tests-and-test-of-independence-being-right-tailed-is-explained,-as-these-tests-are-concerned-with-detecting-observed-frequencies-that-are-greater-than-expected-under-the-null-hypothesis.
Relevant Statistical Tests
- Two-tailed-test:-Applied-when-the-alternative-hypothesis-includes-a-not-equals-symbol,-indicating-that-the-researcher-is-looking-for-evidence-of-a-difference-in-either-direction.
- Right-tailed-test:-Often-used-in-goodness-of-fit-and-tests-of-independence-to-determine-if-observed-frequencies-are-too-high-compared-to-expected-frequencies-under-the-null-hypothesis.
- Left-tailed-test:-This-test-would-be-used-to-determine-if-observed-frequencies-are-too-low-compared-to-expected-frequencies,-which-is-less-common-in-practice.