WorksheetsUnit 5 - II Mat. Stat.
Total questions: 25
Worksheet time: 25mins
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
The rejection region in t-test depends on:
α and df
p-value only
Sample size only
Variance only
F-distribution is used to test:
Mean differences
Equality of variances
Equality of means
Correlation
F-distribution is always:
Negative
Symmetric
Positively skewed
Uniform
The numerator and denominator in F-test represent:
Means
Sample sizes
Variances
Medians
The formula for F-statistic is:
s1 / s₂
s₁² / s₂²
s₂² / s₁²
s₁ + s₂
F-test is sensitive to:
Outliers
Equal means
Equal medians
Data transformation
Degrees of freedom in F-distribution are:
One
Two
Three
None
The F-distribution arises from:
Ratio of means
Ratio of variances
Ratio of correlations
Chi-square differences
The null hypothesis in correlation testing is:
ρ = 0
ρ ≠ 0
ρ > 0
ρ < 0
Chi-square test is:
Exact
Parametric
Non-parametric
Interval based
The formula for chi-square is:
Σ(O - E) / E
Σ(O - E)² / E
Σ(O - E)²
ΣOE
The degree of freedom for chi-square in r × c table is:
r × c
r + c – 1
(r – 1)(c – 1)
Chi-square test is valid only if:
Expected frequency ≥ 5
Sample is small
Frequencies are continuous
Mean equals median
Correlation coefficient ranges between:
–2 to 2
0 to 1
–1 to 1
–∞ to ∞
If observed frequencies deviate greatly from expected:
Test not valid
Reject H₀
Redraw table
Accept H₀
