Question

Math

Posted 5 months ago

```
Here are two different samples drawn from two different populations:
Which sample satisfies the normal condition for constructing a $t$ interval?
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 5 months ago

Solution by Steps

step 2

The Central Limit Theorem states that for a sufficiently large sample size, typically $n \geq 30$, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution

step 3

Sample A has $n=7$, which is less than 30, and the distribution is skewed. This does not satisfy the normal condition for constructing a $t$ interval

step 4

Sample B has $n=36$, which is greater than 30, and the distribution appears to be more symmetrical. This sample size is large enough to satisfy the normal condition for constructing a $t$ interval, assuming random sampling and independence

step 5

Therefore, only Sample B satisfies the normal condition for constructing a $t$ interval

1 Answer

B

Key Concept

Normal Condition for $t$ Intervals

Explanation

For constructing a $t$ interval, the sample should be large enough (usually $n \geq 30$) or the distribution should be approximately normal if the sample size is smaller.

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