Unit 5 - II Mat. Stat.

The t-distribution is used when:

• Sample size is large

• Population variance is known

• Sample size is small and population variance is unknown

• The data is non-numeric

The t-distribution approaches the normal distribution as:

• Degrees of freedom increase

• Sample size decreases

• Variance increases

• Mean becomes zero

For a t-distribution, degrees of freedom is:

• n + 1

• n

• n - 1

• 2n

For testing the difference of two means using t-test, the samples must be:

• Independent

• Dependent

• Always equal

• Large

The formula for one-sample t-test statistic is:

• t = x̅ - μ / s /√n

• t = x̅ + μ

• t = s / x̅

• t = μ / x̅

In small samples, the standard deviation used is:

• σ

• Sample standard deviation (s)

• Mean

• Variance

A paired t-test is used when:

• Two groups are independent

• Two groups are the same and matched

• Population is known

• n > 30

A t-test assumes:

• Population is not normal

• Sample is biased

• Population is normally distributed

• Standard error is zero

If p-value < α in t-test:

• Accept H₀

• Reject H₀

• Do nothing

• Increase α

The value of t depends on:

• Mean and variance only

• Sample size only

• Mean, variance, and sample size

• Mean and correlation