Chapter 7: Sampling and Sampling Distributions
What is the difference between a population and a sample?
A population is the full group of interest; a sample is a subset of that population.
What is the general structure of a confidence interval?
Point estimate ± margin of error
What does the null hypothesis usually represent?
The default position, status quo, or no-change claim
When comparing two unrelated groups, what type of sampling situation are we usually dealing with? (Dependent or Independent)
Independent samples
When comparing two categorical groups, what are we usually comparing?
Two population proportions
In regression analysis, what is the response variable?
The outcome variable being predicted or explained
What type of bias occurs when certain groups are systematically left out of the sample?
Selection bias
If the population standard deviation is known, should we use z or t for a confidence interval for the population mean?
z
Which hypothesis contains the research claim we are trying to find evidence for?
The alternative hypothesis
When comparing before-and-after results from the same subjects, what method should be used?
Matched-pairs procedure
What is the point estimator for the difference between two population proportions?
p̂1 − p̂2
In regression analysis, what is a predictor variable?
A variable used to explain or predict the response variable
What type of bias occurs when people who respond to a survey differ systematically from people who do not respond?
Nonresponse bias
If the population standard deviation is unknown, should we usually use z or t for a confidence interval for the population mean?
t
Which hypothesis always contains some form of equality, such as =, ≤, or ≥?
The null hypothesis
What is the point estimator for the difference between two population means?
x̄1 − x̄2
In a two-proportion hypothesis test where H0 assumes the proportions are equal, what estimate is used in the standard error?
The pooled proportion
Can standard regression analysis prove cause-and-effect relationships?
No
In a stratified random sample, what must happen after the population is divided into strata?
A random sample is taken from each stratum, usually in proportion to the stratum’s size.
What happens to the margin of error when the confidence level increases, holding everything else constant?
The margin of error increases.
If the claim says the population mean is “greater than” a value, what type of test is it? (two-tailed, one-tailed, right-tailed, left-tailed)
Right-tailed test
If population variances are unknown but assumed equal, what type of two-sample t procedure is used?
Pooled-variance t procedure
Is the pooled proportion used for confidence intervals for the difference between two proportions?
No. A pooled proportion is used only in a hypothesis test when the null assumes the two proportions are equal. For a confidence interval, we are estimating the actual difference between the two proportions, so we keep p^1 and p^2 separate.
In the simple regression model y = β0 + β1x + ε, what are β0 and β1?
Unknown population parameters
In a cluster sample, what is randomly selected?
Entire clusters or groups
What happens to the width of a confidence interval when the sample size increases, holding everything else constant?
The interval becomes narrower.
If the claim says the population mean is “less than” a value, what type of test is it?
Left-tailed test
If population variances are unknown and not assumed equal, should we pool the variances?
No
If a confidence interval for p1 − p2 contains 0, what does that suggest?
No clear evidence of a difference between the population proportions
What does the slope coefficient tell us in simple linear regression?
The expected change in y for a one-unit increase in x
What does the central limit theorem say happens to the sampling distribution of the sample mean as sample size increases?
It becomes approximately normal.
What does a 95% confidence level mean in repeated sampling?
About 95% of intervals constructed this way would contain the true population parameter.
If the claim says the population mean is “different from” a value, what type of test is it?
Two-tailed test
If a confidence interval for μ1 − μ2 contains 0, what does that suggest?
There is not sufficient evidence of a difference between the means.
What distribution is used for the test statistic in a two-proportion hypothesis test?
Standard normal, or z distribution
What is a residual?
The observed value minus the predicted value, y − ŷ
What is the formula for the standard error of the sample mean?
σ / √n
Why is it incorrect to say there is a 95% probability that μ is in one specific interval?
μ is fixed; the interval either contains it or it does not.
What is a Type I error?
Rejecting the null hypothesis when it is actually true
If a confidence interval for μ1 − μ2 is entirely positive, what does that suggest?
Population 1 likely has a larger mean than population 2.
What type of test is used to compare observed category counts to expected category counts?
Chi-square goodness-of-fit test
What does ordinary least squares minimize?
The sum of squared residuals, or SSE
If the population standard deviation is 12 and the sample size is 36, what is the standard error of the sample mean?
2
σ / √n.
Here, σ = 12 and n = 36, so standard error = 12 / √36 = 12 / 6 = 2.
What Excel function can be used to find the margin of error for a population mean when σ is known?
CONFIDENCE.NORM
What is a Type II error?
Failing to reject the null hypothesis when it is actually false
In many two-mean hypothesis tests, what is the hypothesized difference d0?
0
What type of test is used to determine whether two categorical variables are related?
Chi-square test for independence
In multiple regression, how do we interpret a slope coefficient?
The expected change in y for a one-unit increase in that predictor, holding other predictors constant
For a sample proportion, what are the two conditions for using the normal approximation?
np ≥ 5 and n(1 − p) ≥ 5
What Excel function can be used to find the margin of error for a population mean when σ is unknown?
CONFIDENCE.T
What decision should be made when the p-value is less than α?
Reject the null hypothesis.
What method is used when comparing the means of three or more groups?
One-way ANOVA
In a chi-square goodness-of-fit test, what is the lowest possible value of the chi-square test statistic?
0
What does R Square measure?
The proportion of variation in the response variable explained by the regression model
What type of control chart is used to monitor a sample proportion for a categorical variable?
p-chart
For a confidence interval for a population proportion, what is the point estimate?
The sample proportion, p-hat
Why do we say “fail to reject” instead of “accept” the null hypothesis?
Because not rejecting H0 does not prove H0 is true.
In ANOVA, what does a small p-value suggest?
At least one population mean differs from the others.
In a test for independence, what does the null hypothesis state?
The two categorical variables are independent, or not related.
If a regression coefficient has a p-value less than 0.05, what do we usually conclude at the 5% significance level?
The coefficient is statistically significant.