stats chapter 9

the conclusions of a hypothesis test that are drawn from the p-value approach versus the critical value approach are

always the same

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

be rejected since the p-value=0.0606<0.10

which statement is not correct concerning the p-value and critical value approaches to hyp testing

both approaches use the same decision rule concerning when to reject Ho

which is not a step we use when formulating the null and alternative hypotheses

calculate the value of the sample statistic

in general, the null and alternative hypothesis are

mutually exclusive

a two 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 should

not be rejected since the p-value = 0.1212 > 0.10

hypothesis testing enables us to determine if the collected ___ data is inconsistent with what is stated in the null hypothesis

sample

for an alternative hypothesis of Ha: u > uo, we might possibly reject the null hypothesis if

the sample mean is greater than uo

the critical value of a hypothesis test is

the value that separates the rejection region from the non-rejection region

T/F: for a given sample size n, a type 1 error can only be reduced at the expense of a higher type 2 error

true

T/F: we choose a value for a before conducting a hypothesis test

true

for a hypothesis test of u when ó is known, the value of the test statistic is calculated as

z = (x- - uo)/ (ó/sqrt n )

which of the following is true

a=the prob of committing a type 1 error. B=the prob of committing a type 2 error

specify the competing hypotheses that would be used in order to determine whether the population mean differs from 15

Ho: u=15, versus Ha: u =/ 15

suppose you are performing a hypothesis test on u and the value of ó is known. At the 5% significance level, the critical value(s) for a two tailed test is (are)

-z0.025 and z 0.025

suppose you are performing a hypothesis test on u and the value of ó is known. At the 10% sig level, the critical value(s) for a left tailed test is (are)

-z0.10

a 95% confidence interval for the mean value of a store's customer accounts is computer as $850 +- 70, then the null hypothesis of a two tailed hypothesis test would be rejected if the value of uo is less than $____ or greater than $____

780, 920

we do not reject the null hypothesis when the p-value is

>= a

the alternative hypothesis for a two sided test for a population mean would be denoted as

Ha: u =/ (not equal) uo

a quality control officer believes that the average time of use for AAA batteries differs from the claimed 8.5 hours. The QC take a random sample of 30 AAA batteries and finds that the sample mean is 8.7 hours. State the null and alt hypothesis for testing the claim

Ho: u = 8.5 Ha: u not equal 8.5

specify the competing hypotheses that would be used to determine whether the population mean is less than 150

Ho: u >= 150 vs Ha: u <150

a type 1 error is commonly denoted as

a (alpha)

the significance level is the probability of making

a type 1 error

the alternative hypothesis

contests the status quo for which a corrective action may be required

the two equivalent methods to solve a hypothesis test are the

critical value approach p-value approach

suppose the competing hypotheses for a test are Ho: u <= 10 vs Ha: u >10. If the value of the test statistic is 1.90 and the CV at the 1% sig level is z 0.01 = 2.23, then the correct conclusion is

do not reject Ho and conclude that the pop mean does not appear to be greater than 10 at the 1% sig level

suppose the competing hypothesis for a test are Ho: u=100 vs Ha: u =/ 100. If the p-val for the hyp test is 0.07 and the chosen level of sig is 0.05, then the correct conclusion is

do not reject Ho and conclude that the population mean does not differ from 100 and the 5% sig level

a type 2 error occurs when we

do not reject the null hypothesis when it is actually false

if the value of the test statistic falls in the rejection region, the p-value must be

less than a

when testing u, the p-value is the probability of obtaining a sample mean at least as large or at least as small as the one derived from a given sample, assuming the ___ hypothesis is true

null

the p-value is calculated assuming the

null hypothesis is true

when performing a hypothesis test on u, the p-value is defined as the

observed probability of making a type 1 error

we can reject the null when the

p-value < a

suppose the competiting hypotheses for a test are Ho: u<= 33 vs Ha: u>33. If the p-value for the hypothesis test is 0.027 and the chosen level of significance is 0.05, then the correct conclusion is

reject Ho and conclude that the population mean is greater than 33 at the 5% sig level

in hyp testing, if the sample data provides significant evidence that the null hyp is incorrect, then we

reject the null hyp

the type 1 error occurs when we

reject the null hypothesis when it is actually true

in hypothesis testing, two correct decisions are possible

rejecting the null hypothesis when it is false not rejecting the null when it is true

the critical value approach specifies a region of values, called the ___. If a test statistic falls into this region, we reject the ___

rejection region, null hypothesis

when testing u and ó is known, Ho can never be rejected if z <= 0 for a

right tailed test

in inferential stats, we use ____ information to make inferences about an unknown ____ parameter

sample, population

put the following steps in the p-value approach to hypothesis testing in the correct order.

specify the null and alternative hypothesis specify the significance level calculate the value of the test statistic and its p-value state the conclusion and interpret results

the null hypothesis in a hypothesis test refers to

the default state of nature

T/F: the optimal values of type 1 and type 2 errors requires a compromise in balancing costs of each type of error

true

when performing a hyp test on u when ó is known, Ho can never be rejected if

z >= 0 for a left-tailed test

an auditor for a small company suspects that the mean customer account balances have fallen below $550 per month, the bag amount for all customer accounts over the past 5 years. She takes a random sample of 40 accounts and computes the sample mean as $543. State the hypothesis for testing the auditors claim

Ho: u >= 550 and Ha: u < 550

in hypothesis testing, two incorrect decisions are possible

Not rejecting the null hypothesis when it is false Rejecting the null hypothesis when it is true