Chapter 10
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
