STAT 203 FINAL EXAM QUESTIONS
AND ASNWERS
What do we assume when testing a hypothesis? - ANSWER-we assume that the null
hypothesis is true and we evaluate whether the evidence presented by the data is
compatible or incompatible with the null hypothesis
What do we have to check in order for the Normal approximation to be true for the
sample proportion p̂ in the Null model? - ANSWER-check that the sample size is
sufficiently large --> np0>/= 10 and n(1-p0) >/= 10
What is a test statistic? - ANSWER-the z-score of the observed sample proportion
for testing a population proportion for the null model
If the test statistic is extremely positive or negative______ - ANSWER-The observed
difference is large and is unusual under the null model. This then suggests that the
data are incompatible with the null hypothesis.
How do we evaluate how unusual an observed difference is when the null model is
true? - ANSWER-We compute the P-value. This is defined as the probability of
getting a value for the test statistic(or sample proportion) that is as extreme as or
more extreme than the observed test statistic assuming that H0 is true.
The smaller the P-value ... - ANSWER-the stronger the evidence against the null
hypothesis is
What does a small P-value suggest? - ANSWER-That what we observe is unlikely to
be due to chance variation if H0 is true. In other words, the data are incompatible
with H0.
What kind of probability is the P-value? - ANSWER-this is a conditional probability.
(condition = null hypothesis is true)
How do we make a decision about whether to reject the null hypothesis? -
ANSWER-If the P-value is smaller than alpha, we reject the null hypothesis and the
test is considered significant at the given alpha level.
- We conclude that the population parameter is significantly different/larger/smaller
than the value specified under H0.
If the P-value is greater than or equal to alpha, we do not reject the null hypothesis
and the test is considered insignificant at the given alpha level.
-We conclude that the population parameter is not significantly
different/larger/smaller than the value specified under H0.
What is an alpha level/ significance level? - ANSWER-denoted by alpha, it sets the
criterion for the decision to reject the null hypothesis. Common alpha values = 0.01,
0.05, 0.1
, What kind of errors can happen in hypothesis testing? - ANSWER-Type 1 and Type
II errors
What is the Type I error? - ANSWER-the mistake of rejecting H0 when H0 is true
What is the Type II error? - ANSWER-the mistake of failing to reject H0 when H0 is
false.
What are the properties of a confidence interval? - ANSWER-centered at the sample
proportion p̂
the width of a CI increases with the confidence level, and hence lower precision
the width of the CI decreases with the sample size hence greater precision (when
the sample size is doubled, the standard error decreases by a factor of sort(2)
How can we interpret a confidence interval for p? - ANSWER-- Over the collection of
all confidence intervals of a fixed confidence level C that could be constructed from
repeated random samples of size n obtained from the population, the percentage of
confidence intervals that contain the true proportion p equals to C
- We are C% confidence that the true proportion falls within the confidence interval
that one has obtained.
What are CI's constructed for? - ANSWER-For parameters not statistics (p not p̂)
Why do we need to determine an appropriate sample size n? - ANSWER-with the
intention of estimating a population proportion, we need to achieve a certain
precision in the estimate of the population parameter. We need to specify the
maximum tolerable margin of error and the confidence level to find the required
sample size.
When calculating sample size, what do we use for p̂? - ANSWER-If we have
estimate of the population proportion from previous studies, we can use those values
for sample size calculation.
If there are no prior studies, we will use p̂ = 0.5 for computing the requires sample
size.
What is a hypothesis? - ANSWER-a statement or a claim about a parameter (a
numerical characteristic of a population)
What is a null hypothesis? - ANSWER-a statement about the value of a population
parameter whose general form is:
H0 : population parameter = some specific value
For population proportion p --> H0 : p = p0
p 0 is some fixed value of p
What does the null hypothesis say? - ANSWER-it states that an observed difference
is due to chance variation not a significant difference.
What is an alternative hypothesis? - ANSWER-It is a statement that opposes the null
hypothesis and states that an observed difference is real.
3 possible forms:
AND ASNWERS
What do we assume when testing a hypothesis? - ANSWER-we assume that the null
hypothesis is true and we evaluate whether the evidence presented by the data is
compatible or incompatible with the null hypothesis
What do we have to check in order for the Normal approximation to be true for the
sample proportion p̂ in the Null model? - ANSWER-check that the sample size is
sufficiently large --> np0>/= 10 and n(1-p0) >/= 10
What is a test statistic? - ANSWER-the z-score of the observed sample proportion
for testing a population proportion for the null model
If the test statistic is extremely positive or negative______ - ANSWER-The observed
difference is large and is unusual under the null model. This then suggests that the
data are incompatible with the null hypothesis.
How do we evaluate how unusual an observed difference is when the null model is
true? - ANSWER-We compute the P-value. This is defined as the probability of
getting a value for the test statistic(or sample proportion) that is as extreme as or
more extreme than the observed test statistic assuming that H0 is true.
The smaller the P-value ... - ANSWER-the stronger the evidence against the null
hypothesis is
What does a small P-value suggest? - ANSWER-That what we observe is unlikely to
be due to chance variation if H0 is true. In other words, the data are incompatible
with H0.
What kind of probability is the P-value? - ANSWER-this is a conditional probability.
(condition = null hypothesis is true)
How do we make a decision about whether to reject the null hypothesis? -
ANSWER-If the P-value is smaller than alpha, we reject the null hypothesis and the
test is considered significant at the given alpha level.
- We conclude that the population parameter is significantly different/larger/smaller
than the value specified under H0.
If the P-value is greater than or equal to alpha, we do not reject the null hypothesis
and the test is considered insignificant at the given alpha level.
-We conclude that the population parameter is not significantly
different/larger/smaller than the value specified under H0.
What is an alpha level/ significance level? - ANSWER-denoted by alpha, it sets the
criterion for the decision to reject the null hypothesis. Common alpha values = 0.01,
0.05, 0.1
, What kind of errors can happen in hypothesis testing? - ANSWER-Type 1 and Type
II errors
What is the Type I error? - ANSWER-the mistake of rejecting H0 when H0 is true
What is the Type II error? - ANSWER-the mistake of failing to reject H0 when H0 is
false.
What are the properties of a confidence interval? - ANSWER-centered at the sample
proportion p̂
the width of a CI increases with the confidence level, and hence lower precision
the width of the CI decreases with the sample size hence greater precision (when
the sample size is doubled, the standard error decreases by a factor of sort(2)
How can we interpret a confidence interval for p? - ANSWER-- Over the collection of
all confidence intervals of a fixed confidence level C that could be constructed from
repeated random samples of size n obtained from the population, the percentage of
confidence intervals that contain the true proportion p equals to C
- We are C% confidence that the true proportion falls within the confidence interval
that one has obtained.
What are CI's constructed for? - ANSWER-For parameters not statistics (p not p̂)
Why do we need to determine an appropriate sample size n? - ANSWER-with the
intention of estimating a population proportion, we need to achieve a certain
precision in the estimate of the population parameter. We need to specify the
maximum tolerable margin of error and the confidence level to find the required
sample size.
When calculating sample size, what do we use for p̂? - ANSWER-If we have
estimate of the population proportion from previous studies, we can use those values
for sample size calculation.
If there are no prior studies, we will use p̂ = 0.5 for computing the requires sample
size.
What is a hypothesis? - ANSWER-a statement or a claim about a parameter (a
numerical characteristic of a population)
What is a null hypothesis? - ANSWER-a statement about the value of a population
parameter whose general form is:
H0 : population parameter = some specific value
For population proportion p --> H0 : p = p0
p 0 is some fixed value of p
What does the null hypothesis say? - ANSWER-it states that an observed difference
is due to chance variation not a significant difference.
What is an alternative hypothesis? - ANSWER-It is a statement that opposes the null
hypothesis and states that an observed difference is real.
3 possible forms:
