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Introductory Statistics

# Chapter Review

### 10.1Two Population Means with Unknown Standard Deviations

Two population means from independent samples where the population standard deviations are not known

• Random Variable: $X ¯ 1 − X ¯ 2 X ¯ 1 − X ¯ 2$ = the difference of the sampling means
• Distribution: Student's t-distribution with degrees of freedom (variances not pooled)

### 10.2Two Population Means with Known Standard Deviations

A hypothesis test of two population means from independent samples where the population standard deviations are known will have these characteristics:

• Random variable: $X ¯ 1 − X ¯ 2 X ¯ 1 − X ¯ 2$ = the difference of the means
• Distribution: normal distribution

### 10.3Comparing Two Independent Population Proportions

Test of two population proportions from independent samples.

• Random variable: $p ^ A – p ^ B = p ^ A – p ^ B =$ difference between the two estimated proportions
• Distribution: normal distribution

### 10.4Matched or Paired Samples

A hypothesis test for matched or paired samples (t-test) has these characteristics:

• Test the differences by subtracting one measurement from the other measurement
• Random Variable: $x ¯ d x ¯ d$ = mean of the differences
• Distribution: Student’s-t distribution with n – 1 degrees of freedom
• If the number of differences is small (less than 30), the differences must follow a normal distribution.
• Two samples are drawn from the same set of objects.
• Samples are dependent.
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