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

Lesson 4: Confidence intervals for the difference of two means

# Constructing t interval for difference of means

Constructing t interval for difference of means.

## Want to join the conversation?

• At , Khan said we should use t-value instead of z-value for better estimations. But from some of the previous videos, I understood only if the sample size is smaller than 30(each group) then we will use t-value? As long as we have more than 30 samples we can use z-score to calculate the difference between means??
• Hi Alexia,

It can be confusing at times because sometimes teachers leave things out when they first teach things, but there are two times when you should use a critical t value instead of a critical z value;
1. When the sample size (n) is less than 30.
2. We are estimating the standard deviation using the Standard Error (S/SE).
NOTE: I believe the 2nd condition only applies when your comparing distributions (like in the video!).

Hope this helps,
- Convenient Colleague
• Why not the same logic was applied for confidence intervals for difference between two proportions? there z value was used even though estimators were used in SD?! Check this https://www.khanacademy.org/math/ap-statistics/two-sample-inference/two-sample-z-interval-proportions/v/confidence-intervals-for-the-difference-between-two-proportions
• through
Why are you estimating the standard deviation of the sampling distribution of sample means with the sample standard deviation? Shouldn't you still divide by the square root of the sample size?
Sigma sub x bar is approximated by s over radical n
σ[x] ~ s/sqrt(n)
(1 vote)
• Why doesn't my dad love me?
(1 vote)
• Why is the variance of the difference between the sample means equal to the sum of the variances of the sample means?
(1 vote)
• whaaat is the difference bn mean and proportions i am baffled
(1 vote)