Chapter 9 Learn Smart
a left-tailed test of the population mean is conducted at a= 0.10. the calculated test statistic is z= -1.55 and P(Z< -1.55) = 0.0606. The null hypothesis should ____.
be rejected since the p-value =0.0606 < 0.10
a binomial distribution can be approximated by a _____ distribution for large sample sizes.
normal
(T/F) in a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.
true
(T/F) the optimal values of Type 1 and Type II errors require a compromise in balancing the costs of each type of error.
true
A type 1 error is commonly denoted as:
a (alpha)
the significance level is the probability of making
a Type 1 error
which of the following is true?
a= the probability of committing a Type 1 error. B= the probability of committing a Type II error.
the following image for the right-tailed test illustrates that the
p-value = P(Z ≥ z)
the alternative hypothesis typically
Contests the status quo and may suggest a corrective action if true.
when testing u, the p-value is the probability of obtaining a sample mean at least as extreme as the one derived from a given sample, assuming that the ______ hypothesis is true.
null
the expected value of the sampling distribution of P- is the _______.
population proportion
put the following steps in the p-value approach to hypothesis testing in the correct order.
1. specify the null and alternative hypotheses 2. calculate the value of the test statistic and its p-value 3. state the conclusion and interpret results
an auditor for a small business wants to test the assumption that the mean value of all accounts receivable differs from $550. She takes a sample of 40 accounts and calculates the sample mean and the sample standard deviation. The null and alternative hypotheses for this test are...
H0: U= $550 and HA : U≠ $550
Specify the competing hypotheses in order to determine whether the population proportion differs from 0.60.
Ho : P= .60 versus HA: P≠ .60
an important final conclusion to a statistical test is to
clearly interpret the results in terms of the initial claim.
consider the following competing hypotheses: H0: u=10 versus HA: u ≠ 10. if a 95% confidence interval is [8.25, 11.55], then at the 5% significant level we
do not reject the null hypothesis and conclude that the population mean does not significantly differ from 10
the two competing hypotheses used in hypothesis testing are called the _____ hypothesis and the _____ hypothesis.
null, alternative
the basic principal of hypothesis testing is to first assume that the ____ hypothesis is true and then determine if the sample data _____ this assumption.
null, contradict
Consider the following competing hypotheses H0: U=10 versus HA: U ≠ 10. If a 95% confidence interval is [15, 20], then at the 5% significance level we ...
reject the null hypothesis and conclude that the population mean appears to differ from 10.
in hypothesis testing, two correct decisions are possible:
reject the null hypothesis when it is false. do not reject the null hypothesis when it is true
in inferential statistics, we are _____ information to make inferences about an unknown ________ parameter.
sample, population
for an alternative hypothesis of HA: u > uo, we might possibly reject the null hypothesis if
the sample mean is greater than Uo
when performing a hypothesis test on u when ó is known H0 can never be rejected if
z ≥ 0 for a left-tailed test.
A quality control officer believes that the average time of use for AAA batteries differs from the claimed 8.5 hours. The QC officer takes a random sample of 30 AAA batteries and finds that the sample mean is 8.7 hours. State the null and alternative hypothesis for testing the officer's claim.
Ho : u= 8.5 Ha: u ≠ 8.5
A researcher for a store chair wants to determine whether the proportion of customers who try out the samples being offered is more than 0.15. the null and alternative hypotheses for this test are ...
Ho: p <- 0.15 and HA: P>0.15
if the population standard deviation is unknown, it can be estimated by using ______
S
which one of the following is NOT a step we use when formulating the null and alternative hypotheses?
calculate the value of the sample statistic
as a point estimate of the population proportion, we calculate ______.
p-
the two equivalent methods to solve a hypothesis test are the
p-value approach critical value approach
in a hypothesis test, u0 and p0 are hypothesized values of the _______ mean and the _____ proportion, respectively.
population, population
(T/F) for a given sample size n, a type 1 error can only be reduced at the expense of a higher type II error.
truee
we do NOT reject the null hypothesis when the p-value is
≥a
