STT 231 EXAM 3A – MICHIGAN STATE UNIVERSITY CONFIDENCE INTERVALS, HYPOTHESIS TESTING, CHI-SQUARE, AND INFERENCE EXAM QUESTIONS WITH 100% VERIFIED ANSWERS

STT 231 EXAM 3A – MICHIGAN STATE UNIVERSITY CONFIDENCE
INTERVALS, HYPOTHESIS TESTING, CHI-SQUARE, AND INFERENCE
EXAM QUESTIONS WITH 100% VERIFIED ANSWERS




Question 1
What is a confidence interval generally in the form of?
A. Mean ± variance
B. Statistic ± margin of error
C. Parameter ± standard deviation
D. Estimate ± standard error
Correct Answer: B. Statistic ± margin of error


Question 2
As the confidence level increases, what happens to the confidence
interval?
A. It becomes narrower/more precise
B. It becomes wider/less precise
C. It stays the same
D. It becomes negative
Correct Answer: B. It becomes wider/less precise (because a higher
confidence level requires a larger margin of error)


Question 3
As the sample size increases (for a confidence interval), what happens
to the confidence interval?

,A. It becomes wider/less precise
B. It stays the same
C. It becomes narrower/more precise
D. It becomes negative
Correct Answer: C. It becomes narrower/more precise (because larger
sample size reduces standard error)


Question 4
A confidence interval should never be interpreted as a:
A. Range of plausible values
B. Probability
C. Statement about the parameter
D. Margin of error
Correct Answer: B. Probability


Question 5
Which of the following is an incorrect interpretation of a 95%
confidence interval?
A. We are 95% confident that the true proportion is between 75.6% and
90.4%
B. If we repeated this sampling process many times, 95% of the
intervals would contain the true proportion
C. There is a 95% chance that the actual percent of coffee drinkers at
MSU is between 75.6% and 90.4%
D. The interval was calculated using a method that captures the true
parameter 95% of the time

,Correct Answer: C. There is a 95% chance that the actual percent of
coffee drinkers at MSU is between 75.6% and 90.4% (THIS IS WRONG)


Question 6
When interpreting a confidence interval, what words or phrases should
you look for? (Select all that apply)
A. "95% confident"
B. "If repeated..."
C. "Probability"
D. "Chance"
Correct Answer: A. "95% confident", B. "If repeated..."


Question 7
If 0 is between the confidence interval, what conclusion can be drawn
about the null hypothesis?
A. The null can be rejected
B. The null cannot be rejected
C. The p-value will be less than 0.05
D. The alternative hypothesis is proven true
Correct Answer: B. The null cannot be rejected


Question 8
If 0 is within the confidence interval, what will be true about the p-value
(assuming α = 0.05)?
A. The p-value will be less than 0.05
B. The p-value will be greater than 0.05

, C. The p-value will equal 0.05
D. The p-value cannot be determined
Correct Answer: B. The p-value will be greater than 0.05 (because little
evidence against the null means we cannot reject it)


Question 9
Which of the following is the correct formula for the effect size for a
mean?
A. (x̄₁ – x̄₂) / σ
B. (p̂ ₁ – p̂ ₂) / SE
C. (x̄ – μ) / s
D. (p̂ – p₀) / √(p₀(1-p₀)/n)
Correct Answer: A. (x̄₁ – x̄₂) / σ (Cohen's d)


Question 10
Which of the following is the correct formula for the effect size for a
proportion?
A. (x̄ – μ) / s
B. (p̂ ₁ – p̂ ₂) / √(p̂ (1-p̂ ))
C. (p̂ – p₀) / √(p₀(1-p₀))
D. (x̄₁ – x̄₂) / σ
Correct Answer: C. (p̂ – p₀) / √(p₀(1-p₀))


Question 11
What are the conditions for two-sample inference for proportions?
(Select all that apply)