7.1 Intro to Hypothesis Testing
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