Question

TRUE OR FALSE QUESTIONS:

1. we usually do not know the population standard deviation (σ) so estimate it using the sample standard deviation (s).

2. The t distribution adjusts for increased sampling variability in small samples, it is more appropriate than the z distribution and we use the sample standard deviations (s) to estimate the population standard deviations (σ).

3. If we cant assume that the population standard deviations are equal in both groups (i.e., σ₁ ≠ σ₂), then we use a pooled variance estimate.

4.If the observed standard deviations are equal in both groups (i.e., s₁= s₂), then results from a test using a pooled variance estimate will be similar to the results from a test using a separate variance estimate.

Answer 1

1. we usually do not know the population standard deviation (σ) so estimate it using the sample standard deviation (s).

Sol:

Sample standard deviation is unbiased estimator of population standard deviation.

Answer: true

2. The t distribution adjusts for increased sampling variability in small samples, it is more appropriate than the z distribution and we use the sample standard deviations (s) to estimate the population standard deviations (σ).

Sol:

When population standard deviation is unknown then we use t distribution. t distribution uses sample standard deviation not population standard deviation.

Answer: false

3. If we cant assume that the population standard deviations are equal in both groups (i.e., σ₁ ≠ σ₂), then we use a pooled variance estimate.

Sol:

If we cant assume that the population standard deviations are equal in both groups (i.e., σ₁ ≠ σ₂), then we do not use a pooled variance estimate.

Answer: false

4.If the observed standard deviations are equal in both groups (i.e., s₁= s₂), then results from a test using a pooled variance estimate will be similar to the results from a test using a separate variance estimate.

Answer: true