stat 226 Quiz 6

A p-value smaller than α indicates we have sufficient evidence in the data to believe in the null hypothesis.

False

A p-value smaller than α indicates we have sufficient evidence in the data to prove that the alternative hypothesis is true.

False

A statistical hypothesis test assesses whether a sample statistic will have a certain value.

False

A type I error occurs if we fail to reject an incorrect null hypothesis.

False

A type II error occurs if a correct null hypothesis is rejected.

False

Failing to reject the null hypothesis implies that the initial "claim" is true.

False

If one has a large amount of data that can clearly reject the null hypothesis one will be able to claim that the result is both statistically significant and practically important.

False

If the p-value is greater than α we reject the alternative hypothesis.

False

If the p-value is less than α we reject the alternative hypothesis.

False

If the standard deviation is estimated from the data, then a z-statistic determines the p-value.

False

Rejecting the null hypothesis always implies that one has made an important or meaningful discovery.

False

Statistical tests infer characteristics of the statistic from a sample.

False

The letter "p" in p-value stands for the parameter p.

False

The p-value corresponds to the probability that the alternative hypothesis is false.

False

The p-value corresponds to the probability that the null hypothesis is false.

False

The p-value is the probability that the null hypothesis is true.

False

When doing a hypothesis test, the alternative hypothesis gets the benefit of the doubt, i.e. the alternative hypothesis is the statement that we are going to believe in unless the data suggest otherwise.

False

When testing a hypothesis, typical values for α are 0.90, 0.95, and 0.95.

False

Normal quantile plots are one example of a visual statistical test. What is the alternative hypothesis associated with this test?

NOT Ha: Data are a sample from a normally distributed population.

If incorrectly rejecting H0 (creating a type I error) can prove to be very costly, one might consider:

NOT avoid performing this hypothesis test. NOT increasing the level of alpha.

Choose from the options given below. A [ ] provides an analysis of a specific, hypothesized value for a population parameter.

NOT confidence interval

If I obtain a positive test statistic and my alternative hypothesis is a "greater than µ ", the corresponding p-value will always be ______________ 0.5.

NOT greater than

When deciding on the appropriate level of significance for a hypothesis test it is important to take into account

NOT the costs associated with the Type I error only.

A two-sided hypothesis test fails to reject the null hypothesis when

NOT the sample mean falls inside the corresponding 100(1-α)% confidence interval.

What assumption must apply before using the hypothesis test for testing the population mean?

The observed sample needs to be a simple random sample from the relevant population.

A confidence interval and a two-sided test produce equivalent statistical conclusions.

True

A statistical hypothesis test assesses whether a population parameter will have a certain value.

True

A t-statistic counts the number of estimated standard errors a sample mean is above or below the hypothesized value µ0 .

True

A type I error occurs if a correct null hypothesis is rejected.

True

A type II error occurs if the alternative hypothesis is true and the null hypothesis is not rejected.

True

Hypothesis tests require the same statistical assumptions as confidence intervals.

True

If the p-value is greater than α we fail to reject the null hypothesis.

True

If the p-value is less than α we reject the null hypothesis.

True

Statistical significance does not imply that you have made an important or meaningful discovery.

True

The p-value obtained from any hypothesis test can be stated as the probability of obtaining a test statistic that is the same as the one obtained or more extreme when assuming that the null hypothesis is true.

True

When doing a hypothesis test, the null hypothesis gets the benefit of the doubt, i.e. the null hypothesis is the statement that we are going to believe in unless our data suggests otherwise.

True

When testing a hypothesis, typical values for α are 0.10, 0.05, and 0.01.

True

The α level is a threshold that sets the maximum tolerance for a [ ] error.

Type I error

Imagine John sampled from a non-normally distributed population. From this sample, he produced a normal quantile plot that displayed data points within the acceptable bounds. As a result, John (mistakenly) concluded the population was normally distributed. This is an example of a [ ] error.

Type II

It is considered good statistical practice to set up your null and alternative hypothesis [ ] looking at the data.

before

Choose from the options given below. A [ ] provides a range of parameter values that is consistent with the observed data.

confidence interval

An alternative hypothesis can also be called a:

contradictory hypothesis

If I obtain a positive test statistic and my alternative hypothesis is a "less than µ", the corresponding p-value will always be ______________ 0.5.

greater than

Fill in the blank. A necessary condition for a hypothesis test is that the observed sample is a [ ] sample from the relevant population.

random

Like confidence intervals, statistical tests rely on assumptions about:

randomness of sample distribution of the sample mean