STAT Exam 3
Conditions for ANOVA
1. randomness 2. Normality/large sample 3. equal population standard deviation
For a two-sample t test where n1 = 16 and n2 = 12, what are the appropriate degrees of freedom?
26
margin of error (m)
A table value (multiplier) times standard error; it measures the maximum difference that could exist between p-hat and p at a specified level of confidence
Which of the following IS a possible alternative hypothesis for an ANOVA test? A. Ha: at least one mean is different B. Ha: all means are different C. Ha: μ1 ≠ μ2 ≠...≠μn
A.
What type of graph is used to display categorical data?
Bar chart
Which of the following is NOT a possible null hypothesis for an ANOVA test? A. H0: all means are equal B. H0: μ1 = μ2 = ... = μn C. H0: μ1 = μ2 and μ2 = μ3 and μ1 = μ3
C
True or False: If results are not practically significant, then they are also not statistically significant
False
True or False: If the population proportion is 0.04, the sampling distribution of p̂ for samples of size 100 will be approximately Normal.
False
True or False: In order to perform an analysis of variance (ANOVA), the explanatory variable must be quantitative.
False
True or False: Power is when we fail to reject a true null hypothesis.
False
True or False: The size of the population affects the width of a confidence interval.
False
True or False: To check the normality condition for this test, we should check the stemplot from each variety of corn separately for outliers and skewness.
False
True or False: We compute our p-value assuming the alternative hypothesis is true.
False
What are the appropriate hypotheses to test whether the proportion of those wearing a seat belt who were not injured is greater than the proportion of those not wearing a seat belt who were not injured? Let w represent those wearing a seat belt and nw represent those not wearing a seat belt.
H0: pw = pnw versus Ha: pw > pnw
What type of visual display should be used for a C à Q relationship?
Side-by-side boxplots
When to use a one-sample t test
Testing a claim with sample information
what us a p-value?
The probability of obtaining a sampling statistic as extreme or more extreme given that the null hypothesis is true.
True or False: A grouped bar chart is an appropriate way to display bivariate categorical data.
True
True or False: A large difference between the observed statistic and the null value results in a small p-value.
True
True or False: ANOVA falls under a C → Q role-type classification.
True
True or False: By "alternative hypothesis" we mean the sampling distribution under the assumption that Ha is true
True
True or False: If our results are statistically significant, then the difference between the observed statistic and the null value is too large to be due to chance variation alone.
True
True or False: Shape, center, and spread have no meaning for bar graphs
True
True or False: The "expected" counts for a chi-square test are the counts we expect if the null hypothesis is true.
True
True or False: The test statistic is a measure of how close the sample proportion is to the null value.
True
If our p value is very small we are saying that if the null hypothesis is true then either...
We sampled poorly We got an unlikely sample (Type 1 error) Our assumption that the null hypothesis is true is a bad one
A 90% confidence interval for the difference between the proportion who were not injured while wearing a seat belt and the proportion who were not injured while not wearing a seat belt was found to be (0.0576, 0.0651). Does this confidence interval allow us to say that the two proportions differ significantly at ααα= 0.10?
Yes, because the confidence interval does not include 0.
A 90% confidence interval was found to be (-0.45, -0.13). Suppose that we were instead testing a two-sided hypothesis. Does this confidence interval allow us to say that the two proportions differ significantly at α = 0.10?
Yes, because the confidence interval does not include 0.
What type of graph would work best for displaying the majors of 2000 college freshman?
bar chart
Fill in the blank:The standard deviation of the sampling distribution of p̂ for samples of size 100 is _________ the standard deviation for samples of size 200.
greater than
two-sample inference
intervals and tests for a difference between 2 means (mu1-mu2)
One sample inference
intervals and tests for a mean (mu)
multi-sample inference
intervals and tests for comparisons of 3 or more means
How to check equal population standard deviation
larger s/smaller s < 2
Fill in the blank: For a 95% confidence interval, we are 95% confident that our estimate will not depart from the true population parameter by more than the .
margin of error
Procedure for tests of significance
matched-pairs t-test for means
n1 and n2 are large enough is
n1p1 > 5 and n1(1-p1) > 5 (same for n2)
n is large enough if
np > 10 and n (1-p) > 10
z
number of standard deviations away from the mean
t
number of standard errors away from the mean
Procedure for estimation using confidence intervals
one sample Z confidence interval for proportions
What is the parameter of interest to compare the proportions from two populations?
p1 - p2
p
population proportion (parameter)
p hat
sample proportion (statistic)
How do we display a set of bivariate categorical data?
two-way table
