One-Sample Tests of
Hypothesis

LEARNING OBJECTIVES
1 Define a hypothesis.
2 Explain the five-step hypothesis-testing procedure.
3 Define Type I and Type II errors.
4 Define the term test statistic and explain how it is used.
5 Distinguish between a one-tailed and a two-tailed hypothesis.
6 Conduct a test of hypothesis about a population mean.
7 Compute and interpret a p-value.
8 Conduct a test of hypothesis about a population proportion.

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Define a hypothesis.
Explain the five-step hypothesis-testing procedure.

Hypothesis and Hypothesis Testing
HYPOTHESIS A statement about the value of a population parameter developed for the purpose of testing.
HYPOTHESIS TESTING A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement.

10-3

The Null and Alternate Hypotheses
NULL HYPOTHESIS A statement about the value of a population parameter developed for the purpose of testing numerical evidence.

ALTERNATE HYPOTHESIS A statement that is accepted if the sample data provide sufficient evidence that the null hypothesis is false.

10-4

Important Things to Remember about H0 and H1
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H0: null hypothesis and H1: alternate hypothesis.
H0 and H1 are mutually exclusive and collectively exhaustive.
H0 is always presumed to be true.
H1 has the burden of proof.
A random sample (n) is used to “reject H0”.
If we conclude “do not reject H0”, this does not necessarily mean that the null hypothesis is true, it only suggests that there is not sufficient evidence to reject H0; rejecting the null hypothesis then suggests that the alternative hypothesis may be true.
Equality is always part of H0 (e.g. “=” , “≥” , “≤”).
“≠”, “” are always part of H1.
10-5

Define the Type I and Type II errors.

Decisions and Errors in Hypothesis Testing
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