Stats - null hypothesis and p value

If you are assessing the safety of a vehicle or an airplane, what type of alpha level will you want?

-a very low alpha level

In order to perform a statistical test of the hypothesis, the null must be a statement about what?

-about the value of a parameter for a model

In terms of the person and the disease, what does this mean?

-an infected person is diagnosed disease free

When must you select the alpha level, before or after you look at the data?

-before you look at the data

How can we reduce β for all alternative parameter values?

-by increasing the alpha level

What is one second type of test help you to confirm the results of a hypothesis test?

-confidence intervals

What can be used as a shortcut for hypothesis tests?

-critical values (z*)

What impact does increasing the sample size have on both Type I and Type II error?

-decreases both

Does this make it easier or harder to make Type I errors?

-easier to make Type I errors

As alpha level increases, does it become easier or harder to reject the null?

-easier to reject the null

If we observe a statistic whose P-value based on the null hypothesis is greater than the alpha level, what do we do?

-fail to reject the null hypothesis

True or false: the P-value is the probability that the null hypothesis is true.

-false

What is it tell us the probability of?

-getting results at least as unusual as the observed statistic, given that the null hypothesis is true

What is the value of β?

-harder to assess than the alpha level

Does this make it easier or harder to make Type II errors?

-harder to make Type II errors

As β increases, does the probability of a Type II error increase or decrease?

-increases

What impact does this have on the power of the test?

-increases power

Which type of error is more serious?

-it depends on the situation

What is one disadvantage to using this method?

-it gives us less information about the hypothesis because we don't have the P-value to think about

Reducing the alpha to lower the chance of committing a Type I error will have what impact on a critical value?

-it will move it

When the power is high, we can be confident that we...?

-looked hard enough

Does statistical significance carry with it any sense of practical importance or impact?

-no

Is the test then statistically significant?

-no, it is not

When the P-value falls below the alpha level, we say that the test is...?

-statistically significant

As the probability of a Type II error increase, what happens to the power of the test?

-test will decrease (per the relationship power = 1 - β)

In medical disease testing, what is typically the null hypothesis?

-that a person is healthy

What is the alternative then?

-that he or see has the disease we're testing for

What value corresponds to the likelihood of making a Type I error?

-the alpha level

How do we choose the null hypothesis?

-the appropriate null hypothesis arises directly from the context of the problem; it is dictated by the situation

What value corresponds to the likelihood of making a Type II error?

-the beta level

What is a type II error?

-the null hypothesis is false, but we fail to reject it

What is a type I error?

-the null hypothesis is true, but we mistakenly reject it

Since we know that beta is the probability that a test fails to reject a null hypothesis, what is the power of a test equal to?

-the probability that a test rejects a null hypothesis: 1 - beta

What is the power of a test?

-the probability that it correctly rejects a false null hypothesis

What is the alpha level also known as?

-the significance level

Whenever a study fails to reject its null hypothesis, what comes into question?

-the test's power

If we observe a statistic whose P-value based on the null hypothesis is less than the alpha level, what do we do?

-we reject the null hypothesis

In a jury trial, when does a Type I error occur?

-when a jury convicts an innocent person

In a jury trial, when does a Type II error occur?

-when a jury fails to convict a guilty person

The movement of this critical value will have what impact on β?

-β will increase

In general, a confidence interval with a confidence level of C% corresponds to a two-sided hypothesis test with an alpha level of ____?

In general, a confidence interval with a confidence level of C% corresponds to a two-sided hypothesis test with an alpha level of 100 - C%?

What should you say when you have not found sufficient evidence to reject the null according to the standard that you have established?

-"The data have failed to provide sufficient evidence to reject the null hypothesis." -->don't ever say that you "accept the null hypothesis."

What are four common alpha levels?

-0.10 -0.05 -0.01 -0.001

Medically speaking, what is a Type II error know as?

-a "false negative"

Medically speaking, what is a Type I error known as?

-a "false positive"

In terms of the person and the disease, what does this mean?

-a healthy person is diagnosed with a disease

If you are wondering whether folks prefer their pizza with or without pepperoni, what type of alpha level might you choose?

-a higher alpha level

What is an alpha level?

-the threshold P-value that determines when we reject a null hypothesis

What is one good way to identify both the null and the alternative hypothesis?

-think about the "why" of the situation

What is the only way to reduce both types of error?

-to collect more evidencce

What is one way to keep the names straight?

-to remember that we start by assuming that the null hypothesis is true, so a Type I error is the first kind of error that we could make

Since confidence intervals are naturally two-sided, what type of z-test do they correspond to?

-two-sided z-tests

When we conduct a hypothesis test, what are we really trying to do in terms of the null hypothesis?

-we are trying to detect a false null hypothesis

Since it can be hard to justify the selection of a given alpha level, what value do we often arbitrarily choose?

0.05

When we perform a hypothesis test, what two types of errors can we make?

1. Type I error 2. Type II error

A P-value is actually a ______________ probability.

A P-value is actually a CONDITIONAL probability.

A confidence interval with a confidence level of C% corresponds to a one-sided hypothesis with an alpha level of _____?

A confidence interval with a confidence level of C% corresponds to a one-sided hypothesis with an alpha level of 1/2*(100-C)%?