Chapter 10

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what is a p-value?

A​ p-value is the probability of observing the actual​ result, a sample​ mean, for​ example, or something more unusual just by chance if the null hypothesis is true.

Type 1 error

Rejecting null hypothesis when the null hypothesis is true

p-value

The probability of observing a test statistic as extreme as, or more extreme than, the statistic obtained from a sample, under the assumption that the null hypothesis is true.

According to the​ report, the mean monthly cell phone bill was $49.04 three years ago. A researcher suspects that the mean monthly cell phone bill is different today. The null hypothesis is not rejected.

There is not sufficient evidence to conclude that the mean monthly cell phone bill is different from its level three years ago of $49.04

The probability of observing the experiment​ result, a sample​ mean, for​ example, or something more unusual just by chance if the null hypothesis is true is the definition of

a p-value

Hypothesis

a proposition assumed as a premise in an argument. a statement regarding a characteristic of one or more populations

test statistic

a statistic whose value helps determine whether a null hypothesis should be rejected

Rejecting the null hypothesis when the null hypothesis is true is called​

a type 1 error

level of significance

alpha, is the probability of making a type 1 error

as the probability of a Type 1 error increases

the probability of a Type 2 error decreases, and vice versa

if the data include outliers

the procedure should not be used

statistically significant

when observed results are unlikely under the assumption that the null hypothesis is true, we say the result is statistically significant and we reject the null hypothesis

If the consequences of making a Type I error are​ severe, would you choose the level of​ significance, alphaα​, to equal​ 0.01, 0.05, or​ 0.10?

0.01

A Type II Error is made...

A Type II Error is made when​ there's not enough evidence to reject the null​ hypothesis, but the null hypothesis is not true.

two-tailed test

A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in either tail of its sampling distribution.

left-tailed test

A one-tailed test in which the sample outcome is hypothesized to be at the left tail of the sampling distribution.

right-tailed test

A one-tailed test in which the sample outcome is hypothesized to be at the right tail of the sampling distribution.

hypothesis testing

A procedure, based on sample evidence and probability theory, used to determine whether the hypothesis is a reasonable statement and should not be rejected or is unreasonable and should be rejected.

the​ P-value is the probability that a sample will result in a statistic such as the one obtained if the null hypothesis is true

About 27 in 100 samples will give a sample proportion as high or higher than the one obtained if the population proportion really is 0.5.

Researchers conducted a study and obtained a​ p-value of 0.75. Based on this​ p-value, what conclusion should the researchers​ draw?

Fail to reject the null hypothesis but do not accept the null hypothesis as true either. A high​ p-value indicates that there is not enough evidence to reject the null hypothesis.​ But, it​ doesn't mean the null hypothesis should be accepted as true.

Sample evidence can prove that a null hypothesis is true.

False. Although sample data is used to test the null​ hypothesis, it cannot be stated with​ 100% certainty that the null hypothesis is true. It can only be determined whether the sample data supports or does not support the null hypothesis.

According to the Federal Housing Finance​ Board, the mean price of a​ single-family home two years ago was $299 comma 400299,400. A real estate broker believes that because of the recent credit​ crunch, the mean price has increased since then. The null hypothesis is rejected.

There is sufficient evidence to conclude that the mean price of a​ single-family home has increased from its level two years ago of ​$299,400

If we reject the null hypothesis when the statement in the null hypothesis is​ true, we have made a Type​ _______ error.

Type 1 error

Failing to reject the null hypothesis means the​ p-value must have been greater than the significance level.

What is true regarding the​ p-value from this hypothesis​ test?

Suppose the null hypothesis is rejected. State the conclusion based on the results of the test. Six years​ ago, 12.2​% of registered births were to teenage mothers. A sociologist believes that the percentage has increased since then.

When the null hypothesis is​ rejected, we say that there is sufficient evidence to support the statement. When the null hypothesis is not​ rejected, we say that there is not sufficient evidence to support the statement. We never say that the null hypothesis is true.

null hypothesis

denoted H0 (read "H-naught"), is a statement to be tested. The null hypothesis is a statement on no change, no effect, or no difference and is assumed true until evidence indicates otherwise. To determine a null​ hypothesis, we generally think of​ "no difference" or​ "no effect".

alternative hypothesis

denoted H1 (read "H-one"), is a statement that we are trying to find evidence to support

type 2 error

do not reject the null hypothesis when the alternative hypothesis is true

When testing a hypothesis using the​ P-value Approach, if the​ P-value is​ large, reject the null hypothesis.

false

one-tailed test

left and right tailed tests

practical significance

refers to the idea that, while small differences between the statistic and parameter stated in the null hypothesis are statistically significant, the difference may not be large enough to cause concern or be considered important


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