Download The 5 Steps of a Statistical Hypothesis Test Calculator

The 5 Steps of a Statistical Hypothesis Test
1. State the null hypothesis, H0
2. State the alternative hypothesis, Ha
3. Determine values for the test statistic and the standardized test statistic.
4. Find the P -value. Use the P -value to decide whether or not to reject the null hypothesis.
5. Write the full sentence conclusion (result) of the hypothesis test.
Calculator Facts
(Section 7.2) If your hypothesis test is about a population mean μ , and the value of population
standard deviation σ is known or given, then use your calculator's "z-test" to obtain the p-value
(Section 7.3) If your hypothesis test is about a population mean μ , and the value of population
standard deviation σ is unknown or not given, then use your calculator's "t-test" to obtain the pvalue
(Section 7.4) If your hypothesis test is about a population proportion (percentage) p , then use
your calculator's "1-prop-z-test" to obtain the p-value
The 5 Steps of a Statistical Hypothesis Test
1. State the null hypothesis, H0
2. State the alternative hypothesis, Ha
Two-Tailed Test
Left-Tailed Test
Right-Tailed Test
Sign in the null hypothesis, H0
=
≥
≤
Sign in the alternative hypothesis, Ha
≠
<
>
Note that the null hypothesis always has an equal to (=) or a greater than or equal to (≥ ) or a less than or
equal to (≤ ) sign, and the alternative hypothesis always has a not equal to (≠ ) or a less than (<) or a
greater than (>) sign.
3. Determine values for the test statistic and the standardized test statistic.
What is a test statistic?
De꘬nition
The test statistic is the sample mean, sample proportion or sample variance or standard
deviation (depending on which one of the parameters, μ, p, σ 2 , or σ, you are testing).
What is a standardized test statistic?
De꘬nition
The standardized test statistic is the number of standard deviations that your sample
statistic is above or below the hypothesized mean (of the sampling distribution).
The Empirical Rule tells us that 95% of our test statistics (and standardized test statistics) will be within
1.96 standard deviations of the mean. 5% of test statistics are either less than -1.96 or greater than 1.96.
Formulas used for the Standardized Test Statistic
If the test is about a population mean, μ , with the value of σ given or known, the standardized test
statistic is given by the formula z
=
x̄ − μ0
σ/√n
, where μ0 is the value of the mean selected for the
null hypothesis.
If the test is about a population mean, μ , with the value of σ not given or unknown, the
standardized test statistic is given by the formula t
=
x̄ − μ0
s/√n
If the test is about a population proportion, p, the standardized test statistic is given by the formula
z =
^ − p0
p
−
−−
−
p0 q0
√
n
and q0
, where p0 is the value of the population proportion selected for the null hypothesis
.
= 1 − p0
4. Find the P -value. Use the P -value to decide whether or not to reject the null hypothesis.
What is a p-value?
De꘬nition
The P–value is the probability of getting a value of the test statistic (and standardized test statistic) that is at least as
extreme as the one representing the given sample data, assuming that the null hypothesis is true. One often "rejects
the null hypothesis" when the P–value is less than the predetermined signi꘬cance level (α), indicating that the
observed result would be highly unlikely under the null hypothesis.<\small>
How can I 瓸ⷒnd the p-value?
Run the appropriate test (z-test, t-test or 1-prop-z-test) on your calculator and it gives you the P -value. Draw a picture of the appropriate sampling
distribution. Center the distribution at the value used in the statement of your null hypothesis. Afterwards, label the location of the sample mean
or sample proportion along the x axis. Finally, sketch the graph of the standardized sampling distribution (either the z or t distribution), and label
the location of the test statistic. Draw a vertical line at that location. Then, use the 耀଄owchart below to help you sketch the correct area under the
sampling distribution that represents the p-value.
How do I use the P -value to decide whether or not to reject the null
hypothesis?
If the p-val ≤
α
then reject the null hypothesis.
If the p-val > α then do not reject the null hypothesis.
What is α (alpha)?
De꘬nition
A type I (or α type) error occurs if you reject the null hypothesis (conclude the sample evidence suggests it is false),
when it is really true.
De꘬nition
The level of signi瓸ⷒcance is the maximum probability of committing a type I error. This probability is symbolized by α
(Greek letter alpha). That is, P(type I error) = α.
As a researcher you will preselect a value for the level of signi꘬cance, α. For the problems we do in this class, you will be given a value for α in the
statement of the problem. If you are not given a value of α in the statement of the problem then use a 5% signi꘬cance level (α = 0.05).
5. Write the full sentence conclusion (result) of the hypothesis test. Use the wording from the 耀଄ow chart given below
Hypothesis Test
Conclusion
This means that...
Reject H0
There is convincing evidence against the null hypothesis. If H0 were true, the sample data would be
very surprising.
Fail to Reject H0
There is not convincing evidence against the null hypothesis. If H0 were true, the sample data would
not be considered surprising.
Example 1