Statitistic MCQ from books

Q1. Standard error of the sample mean is

Answer: C

Q2: When n is large and σ2 is unknown, σ2 is replaced in the test statistic by

a) Sample mean

(b) Sample variance
(c) Sample standard deviation

(d) Sample proportion

Answer (b) Sample variance

Q3: Critical region of a test is
(a) rejection region
(b) acceptance region
(c) sample space
(d) subset of the sample space

Answer (a) rejection region

Q4: The critical value (table value) of the test statistic at the level of significance α for a two-tailed large sample test is

Answeer a

Q5 In general, large sample theory is applicable when

(a) n ≥ 100
(b) n ≥ 50
(c) n ≥ 40
(d) n ≥ 30

Answer (d) n ≥ 30

Q6: When H₁ is a one-sided (right) alternative hypothesis, the critical region is determined by
(a) both right and left tails
(b) neither right nor left tail
(c) right tail
(d) left tail

Answer: (c) right tail

Q7. Critical value at 5% level of significance for two-tailed large sample test is
(a) 1.645
(b) 2.33
(c) 2.58
(d) 1.96

Answer: (d) 1.96

Q8: For testing H_σ: μ = 0 against H₁ : μ < μ₀, what is the critical value at σ = 0.01?

(a) 1.645
(b) –1.645
(c) –2.33
(d) 2.33

Answer: (c) –2.33

Q9. The hypotheses testing problem H_σ: ­μ₀ = ­45 against H₁: ­ μ₀ < ­45 be categorized as
(a) left-tailed
(b) right-tailed
(c) two-tailed
(d) one-tailed

Answer: (a) left-tailed

Q10 When the alternative hypothesis is 1 μ ≠ μ₀ the critical region will be determined by

(a) both right and left tails
(b) neither right nor left tail
(c) right tail
(d) left tail

Answer: (a) both right and left tails

Q11. Rejecting H₀, when it is true is called
(a) type I error
(b) type II error
(c) sampling error
(d) standard error

Answer: (a) type I error

Q12: What is the standard error of the sample proportion under H0?

Answer a:

Q13. The test statistic for testing the equality of two population means, when the population variances are known is

Answer c

Q14. When the population variances are known and equal, the statistic

Answer b

Q15. What is the standard error of the difference between two sample proportions, (P_X – P_Y)?

Answer a

Q16. What is level of significance?

(a) P(Type I Error)
(b) P(Type II Error)
(c) upper limit of P(Type I Error)
(d) upper limit of P(Type II Error)

Answr: (c) upper limit of P(Type I Error)

Q17: Large sample test for testing population proportion is valid, when

Answer A

Q18: Large sample test can be applied for two-sample problems, for testing the equality of two population means, when

(a) m + n ≥ 30
(b) m ≥ 30, n ≥ 30
(c) m ≥ 30, m + n ≥ 30
(d) mn ≥ 30

Answer (b) m ≥ 30, n ≥ 30

Q19. Large sample test is applicable, when the parent population is

(a) normal distribution only
(b) binomial distribution
(c) Poisson distribution
(d) any probability distribution

Answer: D

Q20. What is the rejection rule, based on large sample, for testing H0 against one-sided (left) alternative hypothesis

Answer B