7.1 Intro to Hypothesis Testing

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alpha

denotes the level of significance of a hypothesis test, and it is the probability of committing a type I error

t?f If you want to support a​ claim, write it as your null hypothesis.

false. If you want to support a​ claim, write it as your alternative hypothesis. A hypothesis test can only reject or fail to reject the null hypothesis. Failing to reject the null hypothesis does not mean that the null hypothesis is true. So to support a​ claim, the desired result of the test would be to reject the opposite of that claim.​ Thus, the opposite of the claim should be stated as the null​ hypothesis, and the claim should be the alternative hypothesis.

For the statement​ below, write the claim as a mathematical statement. State the null and alternative hypotheses and identify which represents the claim. A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is less than 9 hours.

mu < 9 H0: mu greater than or equal to 9 Ha: mu < 9 The alternative hypothesis Ha​: μ < 9 is the claim.

For the statement​ below, write the claim as a mathematical statement. State the null and alternative hypotheses and identify which represents the claim. A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is less than 3 hours.

mu <3 hours H0: mu > or equal to 3 hours (equality is always null) Ha: mu < 3hours The alternative hypothesis Ha​: μ<3 is the claim.

alternative hypothesis (Hsub-a)

complement of the null hypothesis statement that must be true if H0 is false and it contains a statement of strict inequality (greater than, less than, not equal to)

T/F A large​ P-value in a test will favor a rejection of the null hypothesis.

False. A small​ P-value in a test will favor a rejection of the null hypothesis. The smaller the​ P-value of the​ test, the more evidence there is to reject the null hypothesis.

T/F In a hypothesis​ test, you assume the alternative hypothesis is true.

False. In a hypothesis​ test, you assume the null hypothesis is true.

Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha. sigma = 3

complement: sigma does not equal 3 H0: sigma =3 Ha: sigma does not euqal 3

Null hypothesis (Hsub0)

contains a statement of equality (greather than or equal to, less than or equal to, equal to)

A null and alternative hypothesis are given. Determine whether the hypothesis test is​ left-tailed, right-tailed, or​ two-tailed. H0​:σ ≥ 66 Ha​: σ < 6

always determined by Ha -less than (L tail), greater than (R tail), not equal to (split tail) left-tailed test

Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha. mu greater than or equals 568

complement of the claim: mu < 568 H0: mu greater than or equal to 568 Ha: mu less than 568

What are the two types of hypotheses used in a hypothesis​ test? How are they related?

null and alternative The null hypothesis H0 is a statistical hypothesis that contains a statement of​ equality, such as ≤​, =​, or ≥. The alternative hypothesis Ha is the complement of the null hypothesis. It is a statement that must be true if H0 is false and it contains a statement of strict​ inequality, such as >​, ≠​, or <. They are complements

type II error

occurs if the NULL hypothesis is not rejected when it's false

Type I error

occurs if the NULL hypothesis is rejected when it's true

What are the two decisions that you can make from performing a hypothesis​ test?

reject the null hypothesis fail to reject the null hypothesis


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