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