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WorksheetsUnit 4 II Maths stat
Total questions: 25
Worksheet time: 25mins
The mean of the sampling distribution of the sample mean is:
Always zero
Equal to population mean
Greater than population mean
Sample variance
The standard deviation of the sampling distribution is called:
Variance
Mean deviation
Standard error
Sampling bias
As sample size increases, the standard error:
Increases
Decreases
Remains constant
Becomes zero
The standard error of the sample mean is:
σ
σ/√n
√σ
nσ
The larger the sample size, the:
Less reliable the results
Greater the variability
Smaller the standard error
Larger the standard error
A statistic is:
A population parameter
A function of sample observations
Always equal to the mean
Population data
A sampling distribution becomes normal when:
Sample size is large (Central Limit Theorem)
Population is small
Variance is zero
Mean is zero
Large sample tests are applicable when:
n < 30
n ≥ 30
n = 10
n ≤ 10
In large samples, the test statistic for mean is based on:
Student's t-distribution
F-distribution
Z-distribution
Poisson distribution
For two large independent samples with means x̅1, x̅2 the test statistic is:
Z=x̅1 + x̅2 / σ
Z = x̅1 - x̅2 / √(σ₁²∕n₁ + σ₂²∕n₂)
Z = x̅₁ - x̅₂
Z = σ₁ + σ₂
For testing population mean μ using large sample, test statistic is:
Z = x̅ − μ ∕ σ∕√n
Z = μ - x̅ / √n
Z = x̅ - μ
Z = σ / √n
In large sample tests, Z is:
A t-value
A percentile
A standardized value
A sample size
The null hypothesis in a mean test is typically:
H₀: μ ≠ μ₀
H₀: μ = μ₀
H₀: μ > μ₀
H₀: x̄ = μ
Critical values for Z at 5% level (two-tailed) is:
±1.64
±1.96
±2.33
±2.58
If test statistic lies beyond the critical value:
Reject H₀
Accept H₀
Increase n
Do not reject H₀
A Z-value of 3.2 implies:
Strong evidence against H₀
No evidence against H₀
Accept H₀
Value is incorrect
In large samples, if population is not normal, the sampling distribution:
Becomes uniform
Becomes normal (CLT)
Is not defined
Is Poisson
If calculated Z < critical Z, we:
Reject H₀
Accept H₁
Do not reject H₀
Increase α
The standard error of difference of two means is:
σ
√(σ₁²∕n₁ + σ₂²∕n₂)
σ₁ + σ₂
√n₁ + n₂
A population proportion is denoted by:
μ
p
σ
x̅
For proportion tests, the standard error is:
√pq/n
√p/n
√pq
p/q
In proportion testing, p and q stand for:
Mean and variance
Z-values
Sample means
Success and failure probabilities
The success probability in a binomial distribution is:
x̄
μ
p
σ
In a two-proportion test, if p1 = 0.7, p2 = 0.6, n1 = 100, n2 = 100, pooled p =:
0.6
0.65
0.5
0.7
In testing large sample proportions, if p = 0.5 and n = 100, SE is:
0.05
0.1
√(0.25/100)
√0.5
