Chapter 9
Alternate hypothesis H1
For a binomial distribution, p hat is the number of successes divided by the number of trials. This
can be used as a point estimate for p, the population proportion of successes.
(For more information, review Section 8.3)
Criteria for using normal approximation to binomial, np > 5 and nq > 5
For a distribution with a sufficiently large number of trials, the normal distribution can be used to
approximate the binomial distribution. The number of trials multiplied by the probability of failure
should be greater than 5. The number of trials multiplied by the probability of success should
also be greater than 5, and this value can be used as the mean. Multiply together the number of
trials, the probability of success, and the probability of failure to obtain the variance. Take the
square root of the variance to get the standard deviation.
(For more information, review Section 9.3)
Critical region
The values of a distribution for which we reject the null hypothesis are called the critical region of
the distribution. Depending on the alternate hypothesis, the critical region is located on the left
side, the right side, or both sides of the distribution.
(For more information, review Section 9.2)
Critical value
Critical values are the boundaries of the critical region. Critical values are designated as z0 for
the standard normal distribution.
(For more information, review Section 9.2)
Hypotheses
Hypotheses are assertions that you assume to be true for the purposes of investigation.
(For more information, review Section 9.1)
Hypothesis testing
Hypothesis testing is used to examine the validity of a hypothesis, such as the value of a
parameter estimate. The central question in hypothesis testing is whether or not you think the
value of the sample test statistic is too far away from the value of the population parameter
proposed in the null hypothesis to occur by chance alone.
(For more information, review Section 9.1)
P-value
Assuming the null hypothesis is true, the probability that the test statistic will take on values as
extreme as or more extreme than the observed test statistic (computed from sample data) is
called the P-value of the test. The smaller the P-value computed from sample data, the stronger
the evidence against the null hypothesis.
(For more information, review Section 9.1)
Left-tailed test
A statistical test is left-tailed if the alternate hypothesis states that the parameter is less than
the value claimed in the null hypothesis.
(For more information, review Section 9.1)
Level of significance
The probability with which we are willing to risk a type I error is called the level of significance of
a test. It is denoted by the Greek letter alpha.
(For more information, review Section 9.1)
Null hypothesis H0
The null hypothesis is the statement that is under investigation or being tested. Usually the null
hypothesis represents a statement of "no effect," "no difference," or, put another way, "things
haven’t changed."
(For more information, review Section 9.1)
Power of a test (1 - beta)
The quantity 1 - beta is called the power of the test and represents the probability of rejecting
the null hypothesis when it is, in fact, false.
(For more information, review Section 9.1)
Right-tailed test
A statistical test is right-tailed if the alternate hypothesis states that the parameter is greater
than the value claimed in the null hypothesis.
(For more information, review Section 9.1)
Statistical significance
In statistical work, significance means that at the alpha level of risk, the evidence (sample data)
against the null hypothesis is sufficient to discredit it, so we adopt the alternate hypothesis. We
do not claim that we have "proved" or "disproved" the null hypothesis, only that the probability
of a type I error (rejecting the null hypothesis when it is, in fact, true) is alpha.
(For more information, review Section 9.1)
Two-tailed test
A statistical test is two-tailed if the alternate hypothesis states that the parameter is different
from (or not equal to) the value claimed in the null hypothesis.
(For more information, review Section 9.1)