Question

Math

Posted 4 months ago

```
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
```

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Answer from Sia

Posted 4 months ago

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.

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