STT 231 EXAM 3A REVIEW AND PRACTICE EXAM
What is the formula for the standard error of the sample mean? - Answers :SE = σ / √n.
What is the formula for the confidence interval for a population proportion? - Answers :π̂
± z*√(π̂(1 - π̂) / n) where π̂ is the sample proportion and n is the sample size.
What conditions must be met for the normal approximation to be valid in proportion
tests? - Answers :we need to see at least 10 successes and 10 failures
What is the effect size classification for moderate-to-large effect size? - Answers :0.5-
0.8
What is the effect size classification for large effect size? - Answers :0.5
What happens to the confidence interval if the sample size increases? - Answers :The
confidence interval becomes narrower.
What happens to the confidence interval if the confidence level increases? - Answers
:The confidence interval becomes wider.
What is the relationship between sample size and confidence interval width? - Answers
:Larger sample sizes result in narrower confidence intervals.
What is the formula for the margin of error in a confidence interval? - Answers :Margin
of Error = z* * SE.
What is the expected value in a chi-squared test? - Answers :Expected = (column
total)(row total) / overall total.
What is the shape of a 𝜒² distribution? - Answers :right-skewed then as the degrees of
freedom it comes more symmetrical
What is the standard deviation of a 𝜒²(2) distribution? - Answers :2, multiply the degrees
of freedom by 2 then take the square root
Which statement correctly interprets the 95% confidence interval (0.75, 0.95)? -
Answers :b. With 95% confidence, we estimate the true coffee drinking rate among
MSU students to be between 75% and 95%.
How would a 99% confidence interval for coffee drinkers compare to the 95% interval
(0.75, 0.95)? - Answers :b. wider than
What is the formula for degrees of freedom in a Χ² independence test? - Answers :c. (#
of rows - 1)(# of columns - 1)
, What happens to the width of a confidence interval when a constant is added to all data
points? - Answers :c. the same width as
What are the null and alternative hypotheses to test if the delivery service rate is
different for City A and City B? - Answers :d. H₀: 𝜋₁ - 𝜋₂ = 0 vs. H₁: 𝜋₁ - 𝜋₂ ≠ 0.
What is the observed on-time delivery rate for City A? - Answers :309 out of 368
deliveries.
What is the observed on-time delivery rate for City B? - Answers :202 out of 262
deliveries.
What is the significance of a p-value in hypothesis testing? - Answers :It indicates the
strength of evidence against the null hypothesis.
What does a right-skewed distribution imply about its tail? - Answers :The tail on the
right side is longer or fatter than the left side.
How does increasing the confidence level affect the confidence interval? - Answers :It
makes the interval wider.
What is the interpretation of a confidence interval? - Answers :It estimates the range in
which the true population parameter lies with a certain level of confidence.
What does it mean if a confidence interval does not include zero? - Answers :It
suggests a statistically significant difference.
What is the purpose of a hypothesis test? - Answers :To determine if there is enough
evidence to reject the null hypothesis.
What is the effect of sample size on the confidence interval width? - Answers :A larger
sample size generally results in a narrower confidence interval.
What is the relationship between confidence intervals and hypothesis testing? -
Answers :Confidence intervals can provide a range of values for the parameter, while
hypothesis tests assess specific claims about those parameters.
What is the implication of a confidence interval that is too wide? - Answers :It indicates
less precision in estimating the population parameter.
What is the condition that must be met for results to be considered statistically valid
regarding expected counts? - Answers :There must be an expected count of at least 5
for each level of the categorical variable.
What is the formula for the standard error of the sample mean? - Answers :SE = σ / √n.
What is the formula for the confidence interval for a population proportion? - Answers :π̂
± z*√(π̂(1 - π̂) / n) where π̂ is the sample proportion and n is the sample size.
What conditions must be met for the normal approximation to be valid in proportion
tests? - Answers :we need to see at least 10 successes and 10 failures
What is the effect size classification for moderate-to-large effect size? - Answers :0.5-
0.8
What is the effect size classification for large effect size? - Answers :0.5
What happens to the confidence interval if the sample size increases? - Answers :The
confidence interval becomes narrower.
What happens to the confidence interval if the confidence level increases? - Answers
:The confidence interval becomes wider.
What is the relationship between sample size and confidence interval width? - Answers
:Larger sample sizes result in narrower confidence intervals.
What is the formula for the margin of error in a confidence interval? - Answers :Margin
of Error = z* * SE.
What is the expected value in a chi-squared test? - Answers :Expected = (column
total)(row total) / overall total.
What is the shape of a 𝜒² distribution? - Answers :right-skewed then as the degrees of
freedom it comes more symmetrical
What is the standard deviation of a 𝜒²(2) distribution? - Answers :2, multiply the degrees
of freedom by 2 then take the square root
Which statement correctly interprets the 95% confidence interval (0.75, 0.95)? -
Answers :b. With 95% confidence, we estimate the true coffee drinking rate among
MSU students to be between 75% and 95%.
How would a 99% confidence interval for coffee drinkers compare to the 95% interval
(0.75, 0.95)? - Answers :b. wider than
What is the formula for degrees of freedom in a Χ² independence test? - Answers :c. (#
of rows - 1)(# of columns - 1)
, What happens to the width of a confidence interval when a constant is added to all data
points? - Answers :c. the same width as
What are the null and alternative hypotheses to test if the delivery service rate is
different for City A and City B? - Answers :d. H₀: 𝜋₁ - 𝜋₂ = 0 vs. H₁: 𝜋₁ - 𝜋₂ ≠ 0.
What is the observed on-time delivery rate for City A? - Answers :309 out of 368
deliveries.
What is the observed on-time delivery rate for City B? - Answers :202 out of 262
deliveries.
What is the significance of a p-value in hypothesis testing? - Answers :It indicates the
strength of evidence against the null hypothesis.
What does a right-skewed distribution imply about its tail? - Answers :The tail on the
right side is longer or fatter than the left side.
How does increasing the confidence level affect the confidence interval? - Answers :It
makes the interval wider.
What is the interpretation of a confidence interval? - Answers :It estimates the range in
which the true population parameter lies with a certain level of confidence.
What does it mean if a confidence interval does not include zero? - Answers :It
suggests a statistically significant difference.
What is the purpose of a hypothesis test? - Answers :To determine if there is enough
evidence to reject the null hypothesis.
What is the effect of sample size on the confidence interval width? - Answers :A larger
sample size generally results in a narrower confidence interval.
What is the relationship between confidence intervals and hypothesis testing? -
Answers :Confidence intervals can provide a range of values for the parameter, while
hypothesis tests assess specific claims about those parameters.
What is the implication of a confidence interval that is too wide? - Answers :It indicates
less precision in estimating the population parameter.
What is the condition that must be met for results to be considered statistically valid
regarding expected counts? - Answers :There must be an expected count of at least 5
for each level of the categorical variable.
