Free Estimation MCQs with Answers

• A. Shorter
• B. Wider
• C. Large
• D. Small

Explanation: For a fixed confidence level, a shorter confidence interval is preferred because it gives a more precise estimate of the population parameter. Increasing confidence generally makes the interval wider, so both goals cannot be maximized simultaneously.

• A. Accuracy
• B. Precision
• C. Error
• D. All of above

Explanation: A confidence interval expresses the precision of an estimate by showing a range of plausible parameter values. Accuracy concerns closeness to the true value, which cannot be guaranteed merely by calculating an interval.

• A. Estimate
• B. Test Statistics
• C. Estimation
• D. Sample
• E. Estimator

Explanation: An estimate is the numerical quantity produced after an estimator, such as a formula or rule, is applied to sample data. The estimator is the rule itself, not the resulting quantity.

• A. Constant
• B. Variable
• C. All of above
• D. Non of these

Explanation: A parameter describes a population and has one fixed value, even though that value is usually unknown. A sample statistic, by contrast, can vary from sample to sample.

• A. 652 and . 728
• B. .314 and .652
• C. .798 and .745
• D. None of these

Explanation: For a proportion, the 90% interval is p ± 1.645√[p(1−p)/n]. Substituting p = .69 and n = 400 gives approximately .69 ± .038, or .652 to .728.

• A. x±1.65 6/√n
• B. u±1.95 S/√n
• C. x±1.96 6/√n
• D. ±1.96 6/√n

Explanation: For a 95% large-sample confidence interval for μ, use x̄ ± 1.96σ/√n. The value 1.65 corresponds approximately to a 90% two-sided interval, while 1.95 is not the standard critical value.

• A. C.I.
• B. Point estimator
• C. Parameter
• D. Point estimate

Explanation: A point estimate reports an estimated parameter as one numerical value, such as x̄ = 40. A confidence interval gives a range rather than a single value.

• A. (U)
• B. 6
• C. Ux
• D. 6/√n

Explanation: If x̄ = 40 is used to estimate the population mean, its target is μ. The symbols in the other choices refer to different parameters or to a standard-error expression.

• A. Biased
• B. Parameter
• C. Unbiased
• D. None of these

Explanation: For a random sample, the sample proportion p̂ has expected value equal to the population proportion P, so it is unbiased. This makes it an estimator, not the population parameter itself.

• A. Unbiased
• B. Consistent
• C. Sufficient
• D. Efficient

Explanation: An estimator is unbiased when its expected value equals the parameter it estimates, so E(θ̂)=θ is the defining condition. Consistency concerns convergence as the sample size increases, not equality of expectations.