Statistics and Probability: Confidence Intervals, Hypotheses,
and DistributionsQ uestions And Answers 2025\2026
A confidence interval for the population mean is an interval constructed around
the __. A. Sample mean | B. Level of significance | C. t-test statistic | D. p-value -
CORRECT ANSWER-A. Sample mean
When the population is normally distributed, the population standard deviation σ
is unknown, and the sample size is n = 100, the confidence interval for population
mean μ is based on __. A. The z distribution | B. The t distribution | C. The
binomial distribution | D. The Poisson distribution - CORRECT ANSWER-B. The t
distribution
True or False: The confidence interval for the true average time per connection is
based on the t distribution when the population standard deviation σ is unknown.
A. True | B. False - CORRECT ANSWER-A. True
The t distribution approaches the __ distribution as the sample size __. A.
Binomial; increases | B. Binomial; decreases | C. z; decreases | D. z; increases -
CORRECT ANSWER-D. z; increases
A standard normal distribution has a mean of __ and a standard deviation of __.
A. Zero; zero | B. Zero; one | C. One; one | D. One; zero - CORRECT ANSWER-B.
Zero; one
, For a given hypothesis test, if we do not reject H₀ and H₀ is true, __. A. No error
has been committed | B. A Type I error has been committed | C. A Type II error
has been committed | D. A Type III error has been committed - CORRECT
ANSWER-A. No error has been committed
What is the most commonly used level of significance? A. 0.15 | B. 0.01 | C. 0.10 |
D. 0.05 - CORRECT ANSWER-D. 0.05
As a general guideline, the research question should be stated as the __. A. Null
hypothesis | B. Alternative hypothesis | C. Tentative assumption | D. Hypothesis
the researcher wants to disprove - CORRECT ANSWER-B. Alternative hypothesis
The average life expectancy of tires is 40,000 miles. Management believes a new
production process has increased tire life. Which hypotheses are correct? A. H₀: μ
< 40,000; Hₐ: μ ≥ 40,000 | B. H₀: μ ≤ 40,000; Hₐ: μ > 40,000 | C. H₀: μ > 40,000; Hₐ:
μ ≤ 40,000 | D. H₀: μ ≥ 40,000; Hₐ: μ < 40,000 - CORRECT ANSWER-B. H₀: μ ≤
40,000; Hₐ: μ > 40,000
A filling machine should dispense exactly 12 ounces. Both overfilling and
underfilling require adjustment. Which hypotheses are correct? A. H₀: μ = 12; Hₐ:
μ ≠ 12 | B. H₀: μ ≤ 12; Hₐ: μ > 12 | C. H₀: μ < 12; Hₐ: μ ≥ 12 | D. H₀: μ ≠ 12; Hₐ: μ =
12 - CORRECT ANSWER-A. H₀: μ = 12; Hₐ: μ ≠ 12
__ is rejecting H₀ when H₀ is true. A. A Type I error | B. A Type II error | C. Random
error | D. A Type III error - CORRECT ANSWER-A. A Type I error
__ says that if the sample size is sufficiently large, the sample means are
approximately normally distributed. A. Cluster sampling | B. Sampling error | C.
and DistributionsQ uestions And Answers 2025\2026
A confidence interval for the population mean is an interval constructed around
the __. A. Sample mean | B. Level of significance | C. t-test statistic | D. p-value -
CORRECT ANSWER-A. Sample mean
When the population is normally distributed, the population standard deviation σ
is unknown, and the sample size is n = 100, the confidence interval for population
mean μ is based on __. A. The z distribution | B. The t distribution | C. The
binomial distribution | D. The Poisson distribution - CORRECT ANSWER-B. The t
distribution
True or False: The confidence interval for the true average time per connection is
based on the t distribution when the population standard deviation σ is unknown.
A. True | B. False - CORRECT ANSWER-A. True
The t distribution approaches the __ distribution as the sample size __. A.
Binomial; increases | B. Binomial; decreases | C. z; decreases | D. z; increases -
CORRECT ANSWER-D. z; increases
A standard normal distribution has a mean of __ and a standard deviation of __.
A. Zero; zero | B. Zero; one | C. One; one | D. One; zero - CORRECT ANSWER-B.
Zero; one
, For a given hypothesis test, if we do not reject H₀ and H₀ is true, __. A. No error
has been committed | B. A Type I error has been committed | C. A Type II error
has been committed | D. A Type III error has been committed - CORRECT
ANSWER-A. No error has been committed
What is the most commonly used level of significance? A. 0.15 | B. 0.01 | C. 0.10 |
D. 0.05 - CORRECT ANSWER-D. 0.05
As a general guideline, the research question should be stated as the __. A. Null
hypothesis | B. Alternative hypothesis | C. Tentative assumption | D. Hypothesis
the researcher wants to disprove - CORRECT ANSWER-B. Alternative hypothesis
The average life expectancy of tires is 40,000 miles. Management believes a new
production process has increased tire life. Which hypotheses are correct? A. H₀: μ
< 40,000; Hₐ: μ ≥ 40,000 | B. H₀: μ ≤ 40,000; Hₐ: μ > 40,000 | C. H₀: μ > 40,000; Hₐ:
μ ≤ 40,000 | D. H₀: μ ≥ 40,000; Hₐ: μ < 40,000 - CORRECT ANSWER-B. H₀: μ ≤
40,000; Hₐ: μ > 40,000
A filling machine should dispense exactly 12 ounces. Both overfilling and
underfilling require adjustment. Which hypotheses are correct? A. H₀: μ = 12; Hₐ:
μ ≠ 12 | B. H₀: μ ≤ 12; Hₐ: μ > 12 | C. H₀: μ < 12; Hₐ: μ ≥ 12 | D. H₀: μ ≠ 12; Hₐ: μ =
12 - CORRECT ANSWER-A. H₀: μ = 12; Hₐ: μ ≠ 12
__ is rejecting H₀ when H₀ is true. A. A Type I error | B. A Type II error | C. Random
error | D. A Type III error - CORRECT ANSWER-A. A Type I error
__ says that if the sample size is sufficiently large, the sample means are
approximately normally distributed. A. Cluster sampling | B. Sampling error | C.
