Esha suspects that adults living in the northern part of her town support a new school tax more than adults in the southern part of town. She wants to take samples of adults from both parts of town and perform a twosample $z$ test to see if the proportion who support the tax is significantly higher in the northern part of town.

Which of the following are conditions for this type of test?
Choose all answers that apply:

A The expected counts of adults who do and do not support the tax in both samples are all at least 10.

B The adults in each sample are randomly selected from their population.

C Each sample includes the same number of adults.

Question

Esha suspects that adults living in the northern part of her town support a new school tax more than adults in the southern part of town. She wants to take samples of adults from both parts of town and perform a twosample $z$ test to see if the proportion who support the tax is significantly higher in the northern part of town.

Which of the following are conditions for this type of test?
Choose all answers that apply:

A The expected counts of adults who do and do not support the tax in both samples are all at least 10.

B The adults in each sample are randomly selected from their population.

C Each sample includes the same number of adults.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the conditions necessary for conducting a two-sample $z$ test for comparing proportions. ‖ ‖ step 2 ⋮ Condition A: The expected counts of adults who do and do not support the tax in both samples should be at least 10. ‖ ‖ step 3 ⋮ Condition B: The adults in each sample must be randomly selected from their respective populations. ‖ ‖ step 4 ⋮ Condition C: It is not necessary for each sample to include the same number of adults, although it is often desirable for increased statistical power. ‖ ∻[question number] Answer∻ ⚹ A and B are conditions for this type of test. ⚹ ∻Key Concept∻ ⚹Conditions for a two-sample $z$ test⚹ ∻Explanation∻ ⚹For a two-sample $z$ test comparing proportions, the expected counts in each category should be at least 10, and the samples should be randomly selected. Equal sample sizes are not a requirement, although they can be beneficial.⚹◊What is the formula for the two-sample z-test for comparing proportions in different groups?⍭ Generate me a similar question◊

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