BUS 281: Chapter 9 - Hypothesis Testing

Which one of the following is NOT a step we use when formulating the null and alternative hypotheses? -Include some form of the equality sign in the null hypothesis -Identity the population parameter of interest -Calculate the value of the sample statistic -Determine whether it is one- or a two-tailed test

-Calculate the value of the sample statistic

Suppose the competing hypotheses for a test are H0 : μ≥75 versus HA : μ<75. The value of the test statistic is t24 = -1.33 and the critical value at the 5% level of significance are -t0.05,24 = -1.711. At the 5% significance level the correct conclusion is: -Reject H0 and conclude that the population mean is less than 75 -Do not reject H0 and conclude that the population mean is less than 75 -Reject H0 and conclude that the population mean is not less than 75 -Do not reject H0 and conclude that the population mean is not less than 75

-Do not reject H0 and conclude that the population mean is not less than 75

Suppose the competing hypotheses for a test are H0 : p=0.30 versus HA : p≠0.30. If the value of the test statistic is -1.05 and the critical values at the 5% level of significance are -z0.025 = -1.96 and z0.025 = 1.96, then the correct conclusion is: -Do not reject H0 and conclude that the population proportion does not differ from 0.30 at the 5% significance level. -Reject H0 and conclude that the population proportion does not differ from 0.30 at the 5% significance level. -Do not reject H0 and conclude that the population proportion differs from 0.30 at the 5% significance level. -Reject H0 and conclude that the population proportion differs from 0.30 at the 5% significance level.

-Do not reject H0 and conclude that the population proportion does not differ from 0.30 at the 5% significance level.

A Type II error occurs when we ____ -Do not reject the null hypothesis when it is actually true -Do not reject the null hypothesis when it is actually false -Reject the null hypothesis when it is actually true -Reject the null hypothesis when it is actually false

-Do not reject the null hypothesis when it is actually false

In hypothesis testing, two incorrect decisions are possible: (Check all that apply) -Not rejecting the null hypothesis when it is false -Not rejecting the null hypothesis when it is true -Rejecting the null hypothesis when it is true -Rejecting the null hypothesis when it is false

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

Put the following steps in the p-value approach to hypothesis testing in the correct order. -State the conclusion and interpret results -Calculate the value of the test statistic and its p-value -Specify the null and alternative hypotheses

-Specify the null and alternative hypotheses -Calculate the value of the test statistic and its p-value -State the conclusion and interpret results

An important final conclusion to a statistical test is to -reject the null hypothesis when it is true -publish the results -clearly interpret the results in terms of the initial claim -fail to reject the null hypothesis when it is true

-clearly interpret the results in terms of the initial claim

The alternative hypothesis typically _______________. -states the probability of rejecting the null hypothesis when it is true -contests the status quo for which a corrective action may be required -states the probability of rejecting the null hypothesis when it is false -corresponds to the presumed default state of nature

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

In general, the null and alternative hypotheses are __________ -correlated -multiplicative -additive -mutually exclusive

-mutually exclusive

A binomial distribution can be approximated by a ____ distribution for large sample size -tdf -exponential -normal -uniform

-normal

A two-tailed test of the population mean is conducted at α = 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 -be rejected since the p-value = 0.1212 > 0.10 -not be rejected since the p-value = 0.1212 > 0.10 -not be rejected since the p-value = 0.0606 < 0.10

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

The p-value is calculated assuming the _____________. -Type II error equal zero -Type I error equals zero -null hypothesis is true -alternative hypothesis is true

-null hypothesis is true

When performing a hypothesis test on μ, the p-value is defined as the ______________________ -allowed probability of making a Type II error -observed probability of making a Type II error -observed probability of making a Type I error -allowed probability of making a Type I error

-observed probability of making a Type I error

The two equivalent methods to solve a hypothesis test are the __________ (check all that apply) -population mean approach -p-value approach -critical value approach -standard deviation approach

-p-value approach -critical value approach

The expected value of the sample distribution of p-bar is the -population mean -sample mean -sample proportion -population proportion

-population proportion

Unlike the mean and standard deviation, the population proportion p is a descriptive summary measure that can be used for data that is ____________. -continuous -discrete -qualitative -quantitative

-qualitative

If the chosen significance level is α=.05, then there is 5% chance of -rejecting a false null hypothesis -accepting a false null hypothesis -rejecting a true null hypothesis -accepting a true null hypothesis

-rejecting a true null hypothesis

We use hypothesis testing to ______________. -determine the best business plan -resolve conflicts between two competing opinions -resolve conflicts between two competing opinions -prove a theory

-resolve conflicts between two competing opinions

Hypothesis testing enables us to determine if the collected ___ data is inconsistent with what is stated in the null hypothesis. -sample -population -parameter -alternative

-sample

In inferential statistics, we use ______ information to make inferences about an unknown ______ parameter. -population, sample -sample, sample -population, sample -sample, population

-sample, population

The critical value of a hypothesis test is _____________. -the value that separates the rejection region from the non-rejection region -the value of the test statistic -equivalent to p-value -not dependent on the significance level of the hypothesis test

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

If the 95% confidence interval for the mean value of a store's customer accounts is computed as $850 +- 70, then the null hypothesis of a two-tailed hypothesis test would be rejected if the value of μ0 is less than $ (a) _________ or greater than $ (b) ___________.

a) 780 b) 920

A type 1 error is commonly denoted as: a) α (alpha) b) β (beta) c) 1 - α d) 1 - β

a) α (alpha)