Here are two different samples drawn from two different populations:

Which sample satisfies the normal condition for performing a $t$ test?

Choose 1 answer:
(A) Sample A only
(B) Sample B only
(C) Both samples
(D) Neither sample

Question

Here are two different samples drawn from two different populations:

Which sample satisfies the normal condition for performing a $t$ test?

Choose 1 answer:
(A) Sample A only
(B) Sample B only
(C) Both samples
(D) Neither sample

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Determine if the sample sizes are large enough for the $t$ test. ‖ ‖ step 2 ⋮ Check if Sample A (n=7) satisfies the normal condition. ‖ ‖ step 3 ⋮ Since Sample A is small (n<30) and not normally distributed, it does not satisfy the normal condition. ‖ ‖ step 4 ⋮ Check if Sample B (n=36) satisfies the normal condition. ‖ ‖ step 5 ⋮ Since Sample B is large (n>30), it satisfies the normal condition under the Central Limit Theorem. ‖ ∻1 Answer∻ ⚹ (B) Sample B only ⚹ ∻Key Concept∻ ⚹Normal Condition for $t$ Test⚹ ∻Explanation∻ ⚹For a $t$ test, the sample should be normally distributed or large enough (usually n>30) for the Central Limit Theorem to apply. Sample A is too small and not normally distributed, while Sample B is large enough.⚹◊What formula can be used to test for normality in a sample before performing a t-test?⍭ Generate me a similar question◊

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