STA 261 STUDY GUIDE 2025/2026 QUESTIONS WITH
SOLUTIONS RATED A+
✔✔why the sampling frame should match the population - ✔✔using the sample to draw
conclusions about the population, so the sampling frame needs to be representative of
the population
✔✔sample - ✔✔part of a population
✔✔parameter - ✔✔numerical summary of a population (u, p, sigma)
✔✔statistic - ✔✔numerical summary of a sample (x bar, p hat, s)
✔✔point estimate - ✔✔Single value that serves as an estimate of a population
parameter
✔✔interval estimate - ✔✔interval or range of values within which the true population
value is estimated to fall (confidence interval), includes the point estimate and a margin
of error
✔✔unbiased, small standard deviation - ✔✔two properties of good point estimates
✔✔we are ____ confident that the true ____ of ____ is somewhere between ____ and
___ - ✔✔confidence interval interpretation
✔✔margin of error - ✔✔reflects the precision of the sample statistic as a point estimate
for the parameter, equal to half the width of the CI, also referred to as standard error
✔✔1.645 - ✔✔z-score for confidence level of 90%
✔✔1.96 - ✔✔Z Score for a 95% Confidence Interval
✔✔2.576 - ✔✔Z-score for 99% level of confidence
✔✔randomization, large enough sample (15 successes and 15 failures) -
✔✔assumptions for confidence interval of one population proportion
✔✔higher, less - ✔✔the _____ the confidence interval, the ____ precise my estimate is
of the parameter
✔✔decreases, increases - ✔✔when the confidence level _______, the precision
_______ and vice versa
, ✔✔randomization, normal population or large enough sample size, find any outliers -
✔✔assumptions for one mean interval test
✔✔double - ✔✔the width is equal to ____ of the margin of error
✔✔1-Proportion plus-4 z-interval - ✔✔used with samples sizes less than 10 and
confidence levels less than 90, add 4 to the sample size (2 to successes and 2 to
failures)
✔✔when to use bootstrapping - ✔✔when it is difficult to find the standard error or when
the confidence interval method doesn't work well
✔✔copies - ✔✔bootstrapping population is viewed as many _____ of the original
sample
✔✔resample with replacement - ✔✔step one of bootstrapping
✔✔same - ✔✔bootstrap sample must have the ____ number of observations as the
original data distribution
✔✔resample a very large number of sets of n observations from the original data
sample - ✔✔step 2 of bootstrapping
✔✔create a distribution of the point estimates from the n samples - ✔✔step 3 of
bootstrapping
✔✔standard error method - ✔✔way to find a confidence interval by using standard
deviation of bootstrap distribution -- example: using a 90% CI, take mean +/-
1.695*(stdv)
✔✔percentile method - ✔✔way to find a confidence interval by using the percent and
dividing the remaining portion by two -- example: 95% CI, the two tail areas are 2.5%
✔✔null hypothesis - ✔✔the hypothesis that there is no significant difference between
specified populations, any observed difference being due to sampling or experimental
error.
✔✔alternative hypothesis - ✔✔The hypothesis that states there is a difference between
two or more sets of data.
✔✔two-tailed test - ✔✔to determine whether a population proportion is different from a
specified valued
SOLUTIONS RATED A+
✔✔why the sampling frame should match the population - ✔✔using the sample to draw
conclusions about the population, so the sampling frame needs to be representative of
the population
✔✔sample - ✔✔part of a population
✔✔parameter - ✔✔numerical summary of a population (u, p, sigma)
✔✔statistic - ✔✔numerical summary of a sample (x bar, p hat, s)
✔✔point estimate - ✔✔Single value that serves as an estimate of a population
parameter
✔✔interval estimate - ✔✔interval or range of values within which the true population
value is estimated to fall (confidence interval), includes the point estimate and a margin
of error
✔✔unbiased, small standard deviation - ✔✔two properties of good point estimates
✔✔we are ____ confident that the true ____ of ____ is somewhere between ____ and
___ - ✔✔confidence interval interpretation
✔✔margin of error - ✔✔reflects the precision of the sample statistic as a point estimate
for the parameter, equal to half the width of the CI, also referred to as standard error
✔✔1.645 - ✔✔z-score for confidence level of 90%
✔✔1.96 - ✔✔Z Score for a 95% Confidence Interval
✔✔2.576 - ✔✔Z-score for 99% level of confidence
✔✔randomization, large enough sample (15 successes and 15 failures) -
✔✔assumptions for confidence interval of one population proportion
✔✔higher, less - ✔✔the _____ the confidence interval, the ____ precise my estimate is
of the parameter
✔✔decreases, increases - ✔✔when the confidence level _______, the precision
_______ and vice versa
, ✔✔randomization, normal population or large enough sample size, find any outliers -
✔✔assumptions for one mean interval test
✔✔double - ✔✔the width is equal to ____ of the margin of error
✔✔1-Proportion plus-4 z-interval - ✔✔used with samples sizes less than 10 and
confidence levels less than 90, add 4 to the sample size (2 to successes and 2 to
failures)
✔✔when to use bootstrapping - ✔✔when it is difficult to find the standard error or when
the confidence interval method doesn't work well
✔✔copies - ✔✔bootstrapping population is viewed as many _____ of the original
sample
✔✔resample with replacement - ✔✔step one of bootstrapping
✔✔same - ✔✔bootstrap sample must have the ____ number of observations as the
original data distribution
✔✔resample a very large number of sets of n observations from the original data
sample - ✔✔step 2 of bootstrapping
✔✔create a distribution of the point estimates from the n samples - ✔✔step 3 of
bootstrapping
✔✔standard error method - ✔✔way to find a confidence interval by using standard
deviation of bootstrap distribution -- example: using a 90% CI, take mean +/-
1.695*(stdv)
✔✔percentile method - ✔✔way to find a confidence interval by using the percent and
dividing the remaining portion by two -- example: 95% CI, the two tail areas are 2.5%
✔✔null hypothesis - ✔✔the hypothesis that there is no significant difference between
specified populations, any observed difference being due to sampling or experimental
error.
✔✔alternative hypothesis - ✔✔The hypothesis that states there is a difference between
two or more sets of data.
✔✔two-tailed test - ✔✔to determine whether a population proportion is different from a
specified valued
