MATH 1680 Exam Questions And Answers| Already Graded A+| Latest Update.

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MATH 1680 Exam Questions And Answers|
Already Graded A+| Latest Update.



What is at the "heart" of hypothesis testing in statistics? - Answer✔Make an assumption about
reality, and collect sample evidence to determine whether it contradicts the assumption.

What is a hypothesis? - Answer✔A statement regarding a characteristic of one or more
populations.
Why do we test statements about a population parameter using sample data? -
Answer✔Because it is usually impossible or impractical to gain access to the entire population.

State the definition of hypothesis testing. - Answer✔A procedure based on sample evidence
and probability, used to test statements regarding a characteristic of one or more populations.

List the 3 steps in hypothesis testing. - Answer✔1. Make a statement regarding the nature of
the population.
2. Collect evidence (sample data) to test the statement
3. Analyze the data to assess the plausibility of the statement

State the definition of the null hypothesis. - Answer✔A statement to be tested. The null
hypothesis is a statement of no change, no effect, or no difference and is assumed true until
evidence indicates otherwise.

List the three ways to set up the null and alternative hypotheses. - Answer✔Two tailed test
Equal versus not equal hypothesis
H0 : parameter = some value
H1 : parameter does not equal some value




Left-tailed test

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2. Equal versus less than
H0 : parameter = some value
H1 : parameter < some value




Right-tailed test
3. Equal versus greater than
H0 : parameter = some value
H1 : parameter > some value

What type of tests are referred to as one-tailed tests? - Answer✔Left and right tailed tests
What determines the structure of the alternative hypothesis (two-tailed, left-tailed, or right-
tailed?) - Answer✔The statement we are trying to gather evidence for.

What type of error is called a Type I error? - Answer✔Reject the null hypothesis when the null
hypothesis is true. This decision would be incorrect. This type of error is called a Type I error.

What type of error is called a Type II error? - Answer✔Do not reject the null hypothesis when
the alternative hypothesis is true. This decision would be incorrect. This type of error is called a
Type II error.

In a jury trial, what are the null and alternative hypotheses? - Answer✔Null hypothesis:
innocent
Alternative hypothesis: guilty

What jury decision is associated with rejecting the null hypothesis? - Answer✔Guilty

What jury decision is associated with failing to reject the null hypothesis? - Answer✔Not guilty

Is the null hypothesis ever declared "true"? - Answer✔No, it is either rejected or not rejected

In a jury trial, what decision is equivalent to making a Type I error? - Answer✔Declaring an
innocent person guilty

In a jury trial, what decision is equivalent to making a Type II error? - Answer✔Declaring a guilty
person "not guilty"
What symbols do we use to denote the probability of making a Type I error and the probability
of making a Type II error? - Answer✔α = P(Type I error)=P(rejecting H0 when H0 is true)

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β=P(Type II error) = P(not rejecting H0 when H1 is true)

What does the level of significance represent? - Answer✔The level of significance, α, is the
probability of making a Type I error

What does the choice of the level of significance depend on? - Answer✔The choice of the level
of significance depends on the consequences of making a Type I error. If the consequences are
severe, the level of significance should be small (say, α=0.01). However, if the consequences are
not severe, a higher level of significance can be chosen (say, α=0.05 or α=0.10).

Why is the level of significance not always set at α=0.01 - Answer✔Reducing the probability of
making a Type I error increases the probability of making a Type II error, β. Using our court
analogy from the video explaining Figure 1, a jury is instructed that the prosecution must
provide proof of guilt "beyond all reasonable doubt." This implies that we are choosing to make
α small so that the probability of convicting an innocent person is very small. The consequence
of the small α, however, is a large β, which means many guilty defendants will go free. For now,
we are content to recognize the inverse relation between α and β. (As one goes up, the other
goes down.

It is important to recognize that we never accept the null hypothesis. - Answer✔Sample
evidence can never prove the null hypothesis to be true. By not rejecting the null hypothesis,
we are saying that the evidence indicates that the null hypothesis could be true or that the
sample evidence is consistent with the statement in the null hypothesis.
If the consequences of making a Type I error are severe, would you choose the level of
significance,
α,

to equal 0.01, 0.05, or 0.10? - Answer✔0.01

Give the definition of what it means for a result to be statistically significant. - Answer✔When
observed results are unlikely under the assumption that the null hypothesis is true, we say that
the result is statistically significant and we reject the statement in the null hypothesis.
A criterion for testing hypotheses is to determine how likely the observed sample proportion is:
- Answer✔under the assumption that the statement in the null hypothesis is true.

Give the definition of a P-value. - Answer✔A P-value is the probability of observing a sample
statistic as extreme as or more extreme than one observed under the assumption that the
statement in the null hypothesis is true. Stated another way, the P-value is the likelihood or
probability that a sample will result in a statistic such as the one obtained if the null hypothesis
is true.



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Explain how to determine whether the null hypothesis should be rejected using the P-value
approach. - Answer✔If the probability of getting a sample statistic as extreme as or more
extreme than the one obtained is small under the assumption that the statement in the null
hypothesis is true, reject the null hypothesis.
What are the three conditions that must be satisfied before testing a hypothesis regarding a
population proportion, p? - Answer✔the sample is obtained by simple random sampling or the
data result from a randomized experiment ; np0(1−p0)≥10 where p0 is the proportion stated in
the null hypothesis; and the sampled values are independent of each other. This means that the
sample size is no more than 5% of the population size (n≤0.05N).

State the five steps for testing a hypothesis about a population proportion, p. - Answer✔Step 1:
Determine the null and alternative hypotheses. The hypotheses can be structured in one of
three ways:


Step 2: Select a level of significance, α, depending on the seriousness of making a Type I error .


Step 3 (By Hand) Step 3 (Using Technology): compute the test statistic


Step 4: If P-value <α, reject the null hypothesis.


Step 5: State the conclusion
Explain how to make a decision about the null hypothesis when performing a two-tailed test
using confidence intervals. - Answer✔When testing H0: p=p0 versus H1: p≠p0, if a (1−α)⋅100%
confidence interval contains p0, we do not reject the null hypothesis. However, if the
confidence interval does not contain H0: p=p0 versus H1: p≠p0, if a (1−α)⋅100% confidence
interval contains p0, we do not reject the null hypothesis. However, if the confidence interval
does not contain p0, we conclude that p≠ p0 at the level of significance α.
For the sampling distribution of p^ to be approximately normal, we require that np(1-p) be at
least 10. - Answer✔If this requirement is not satisfied we use the binomial probability formula
to determine the P-value.
When there are small sample sizes, the evidence against the statement in the null hypothesis
must be
__________ One should be wary of studies that _____________ the null hypothesis when the
test was conducted with a small sample size. - Answer✔substantial; do not reject

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