Q.1 What is the main purpose of estimation in statistics?
To guess randomly
To approximate population parameters
To prove hypotheses
To find causal relationships
Explanation - Estimation is used to infer the value of population parameters using sample data.
Correct answer is: To approximate population parameters
Q.2 Which of the following is an example of a point estimate?
Confidence interval
Sample mean
Population variance
Range
Explanation - A point estimate gives a single value, such as the sample mean, to estimate a population parameter.
Correct answer is: Sample mean
Q.3 Interval estimation provides:
A single value
A range of possible values
Only population mean
No useful result
Explanation - Interval estimation provides a confidence interval that indicates the range within which the parameter lies with a given probability.
Correct answer is: A range of possible values
Q.4 Which of the following is true about a 95% confidence interval?
It always contains the true parameter
It contains the true parameter with 95% probability
It guarantees correctness
It is narrower than a 99% confidence interval
Explanation - A 95% confidence interval means that if repeated samples are taken, about 95% of such intervals will contain the true parameter.
Correct answer is: It contains the true parameter with 95% probability
Q.5 In hypothesis testing, the null hypothesis (H0) represents:
The research claim
The assumption of no effect or no difference
The alternative outcome
A guaranteed truth
Explanation - The null hypothesis usually states there is no effect or no significant difference.
Correct answer is: The assumption of no effect or no difference
Q.6 The alternative hypothesis (H1) usually represents:
No difference exists
The researcher's claim
Random error
The null condition
Explanation - The alternative hypothesis is the statement a researcher aims to prove.
Correct answer is: The researcher's claim
Q.7 What is a Type I error?
Accepting a false null hypothesis
Rejecting a true null hypothesis
Accepting a true null hypothesis
Rejecting a false alternative hypothesis
Explanation - Type I error occurs when we wrongly reject a true null hypothesis (false positive).
Correct answer is: Rejecting a true null hypothesis
Q.8 What is a Type II error?
Rejecting a true null hypothesis
Failing to reject a false null hypothesis
Accepting an alternative hypothesis wrongly
Making a calculation mistake
Explanation - Type II error occurs when we fail to reject a false null hypothesis (false negative).
Correct answer is: Failing to reject a false null hypothesis
Q.9 The significance level (α) in hypothesis testing is:
Probability of Type I error
Probability of Type II error
Always equal to 0.5
Confidence level
Explanation - Significance level is the probability of rejecting the null hypothesis when it is true (Type I error).
Correct answer is: Probability of Type I error
Q.10 A smaller p-value indicates:
Stronger evidence against H0
Weaker evidence against H0
No relation to H0
Always acceptance of H0
Explanation - Smaller p-values provide stronger evidence against the null hypothesis.
Correct answer is: Stronger evidence against H0
Q.11 If α = 0.05, what does it mean?
5% chance of Type I error
5% chance of Type II error
Null hypothesis is always false
Test is unbiased
Explanation - α = 0.05 means we allow a 5% probability of rejecting a true null hypothesis.
Correct answer is: 5% chance of Type I error
Q.12 Which test is appropriate for comparing two population means with known variance?
Z-test
Chi-square test
t-test
F-test
Explanation - When population variance is known and sample size is large, Z-test is used for comparing means.
Correct answer is: Z-test
Q.13 Which test is most suitable for small sample mean comparison?
Z-test
t-test
F-test
Chi-square test
Explanation - t-test is applied when the sample size is small and population variance is unknown.
Correct answer is: t-test
Q.14 Chi-square test is mainly used for:
Testing means
Testing variances and independence
Testing regression coefficients
Testing correlations
Explanation - Chi-square test is commonly used for testing independence and goodness-of-fit in categorical data.
Correct answer is: Testing variances and independence
Q.15 The power of a statistical test is defined as:
1 - α
1 - β
α + β
α - β
Explanation - The power of a test is the probability of correctly rejecting a false null hypothesis, equal to 1 - β.
Correct answer is: 1 - β
Q.16 In estimation, increasing the sample size generally:
Increases the confidence level
Decreases the margin of error
Increases bias
Has no effect
Explanation - Larger samples reduce variability, narrowing the confidence interval and reducing error.
Correct answer is: Decreases the margin of error
Q.17 Which of the following is NOT a property of a good estimator?
Unbiasedness
Consistency
Efficiency
Subjectivity
Explanation - Good estimators should be unbiased, consistent, and efficient. Subjectivity is not desirable.
Correct answer is: Subjectivity
Q.18 A confidence interval that is too wide indicates:
High precision
Low precision
High bias
Perfect estimation
Explanation - Wide confidence intervals suggest less precision in estimation.
Correct answer is: Low precision
Q.19 In hypothesis testing, the critical region refers to:
Region of acceptance
Region where H0 is rejected
Area under the entire curve
Middle 95% of distribution
Explanation - The critical region contains values that lead to rejection of H0.
Correct answer is: Region where H0 is rejected
Q.20 What happens if p-value > α?
Reject H0
Fail to reject H0
Always accept H1
Reduce α
Explanation - If the p-value is larger than α, evidence is not strong enough to reject H0.
Correct answer is: Fail to reject H0
Q.21 The t-distribution is similar to the normal distribution but:
Has thinner tails
Has thicker tails
Has no mean
Is uniform
Explanation - t-distribution accounts for extra variability in small samples and has thicker tails.
Correct answer is: Has thicker tails
Q.22 Which distribution is used in hypothesis tests for variance?
Normal
t-distribution
Chi-square
Binomial
Explanation - The chi-square distribution is commonly used in testing population variances.
Correct answer is: Chi-square
Q.23 If a test is unbiased, it means:
Expected value of estimator = true parameter
Estimator always equals true value
Estimator has minimum variance
Sample is random
Explanation - Unbiasedness means the estimator's expected value equals the population parameter.
Correct answer is: Expected value of estimator = true parameter
Q.24 The F-test is primarily used for:
Comparing means of two groups
Comparing variances of two groups
Testing correlation
Testing independence
Explanation - F-test is mainly used to compare two population variances.
Correct answer is: Comparing variances of two groups
Q.25 Which of the following decreases with a higher confidence level?
Margin of error
Sample size
Width of confidence interval
Precision
Explanation - Higher confidence levels increase the width of the interval, reducing precision.
Correct answer is: Precision