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## AP®︎/College Statistics

### Course: AP®︎/College Statistics > Unit 11

Lesson 4: Confidence intervals for the difference of two means- Conditions for inference for difference of means
- Conditions for inference on two means
- Constructing t interval for difference of means
- Calculating confidence interval for difference of means
- Two-sample t interval for the difference of means (calculator-active)

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# Conditions for inference for difference of means

AP.STATS:

UNC‑4 (EU)

, UNC‑4.W (LO)

, UNC‑4.W.1 (EK)

Conditions for inference for difference of means.

## Want to join the conversation?

- If you take n > 30, then no more t statistic needed in CI, one could use z?!(1 vote)

## Video transcript

- [Instructor] A food
scientist wants to estimate the difference between
the mean weights of eggs classified as jumbo and large. They plan on taking a
sample of each type of egg to construct a two-sample t interval. Which of the following are conditions for this type of interval? So before I even look at these choices, and they say choose
all answers that apply, so it might be more than one, let's just think about what the conditions for inference for this type
of interval actually are. So we've done this many times
in many different contexts, and so we first of all
have the random condition. And that's the idea
that each of our samples are random or we are conducting
some type of an experiment where we randomly assign folks
to one or eggs in this case to one of two groups. In this case we are taking two samples, and we would hope that they
are truly random samples. The second is the normal condition, and the normal condition
is a little bit different depending on whether
we're talking about means or whether we're talking
about proportions. The random condition is
essentially the same. The normal condition when
we're talking about means, remember they're looking at the difference between mean weights of eggs, is you would want your, there's actually several ways
to meet the normal condition. One is is if the underlying
distribution is normal. The second way is if your sample sizes for each of your samples are
greater than or equal to 30. So if your first sample size
is greater than or equal to 30 and your second sample size is
greater than or equal to 30. Or even if the underlying
data you don't know if it's normal or if it isn't normal, and even if you aren't able to meet these, as long as your sample
data is roughly symmetric and not skewed heavily
in one way or the other, then that also roughly
meets the normal condition when we're dealing with means. And then the third condition, and we see this whether
we're dealing with means or proportions or differences of means or differences of proportions, is the independence condition. And this is the idea that either your individual observations
are done with replacement in both of your samples or that the sample size
for both of your samples is no more than 10% of the population. Then you have met this condition. So with that little bit of a review, let's see which of these apply. They observe at least 10
heavy eggs and 10 light eggs in each sample. So this actually is the normal condition when we are dealing with
proportions, not for means. So I would rule this out. It's a good distractor choice. The eggs in each sample
are randomly selected from their population. Yep, that's the random
condition right over there, so I would select that. They sample an equal
number of each type of egg. So this is a common misconception, that whether we're dealing
with means or proportions, when we're thinking about the
difference between say means or the difference between proportions, that somehow your sample sizes
have to be the exact same. That is not the case. Your sample sizes do not
have to be the exact case. Or do not have to be the exact same. So we would rule this out as well. So right over here, they have listed the random condition. They could've also listed
the normal condition and the independence condition.