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

Question

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

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine which sample satisfies the normal condition for constructing a $t$ interval, we need to consider the sample size and the shape of the distribution. ‖ ‖ 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.⚹◊What is the formula for calculating the confidence interval for the difference between two population proportions?⍭ Generate me a similar question◊

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