Significant Difference Test (Means)

▶ Back to previous note on: One-sample T test

Reminder: One-sample T Test

Formula for Two-sample T Test

The difference μ1 - μ2 comes from the null hypothesis. In this type of test, we assume μ1 = μ2 in the population means, which results in μ1 - μ2 =0.

T-value for Two-sample Test

Example

Solve:

P-value for Two-sample Test

For the Degree of freedom in the Two-sample Test, we’re gonna use the SMALLERsample size.

Example

Solve:

• Calculate the t-value to get t=2.12621542
• Decide df, which will be the smaller sample size 46- 1 = 45
• Since it’s asking Ha: μ1 ≠ μ2, so we're to calculate both tails:

• Get an online calculator and input the values:

Use CI to make conclusions about the difference of means

▶︎ Back to previous note: Significance Testing

Normally, we can make conclusion simply by comparing P-value with Significance level.

But there’re cases ask us to make conclusion by comparing Confidence level with Significance level.
In that case, we can judge it by simply examine whether the Confidence intervalcovers 0 or not.

Since Confidence Level + Significance Level = 100%:

• CI exlcudes 0 ▶ Smaller interval & larger significance ▶ Significance level > P-value ▶ Not reject
• CI includes 0 ▶ Larger interval & smaller significance ▶ Significance level < P-value ▶ Reject

Example

Solve:

• No, because the P-value > ⍺, means there's no sufficient evidence against the null hypothesis.

Example

Solve:

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