BNAD 276: TEST 3

An auditor for a small company suspects that the mean customer account balances have fallen below $550 per month, the average amount for all customer account 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: μ ≥ 543 and Ha: μ < 543 - Ho: μ ≥ 550 and Ha: μ < 550 - Ho: μ < 550 and Ha: μ ≥ 550 - Ho: μ < 543 and Ha: μ ≥ 543

- Ho: μ ≥ 550 and Ha: μ < 550 Ho signs: (≥) (≤) (=) ha signs: (<) (>) (≠)

Set up the hypothesis

- always start with the Ha (Alternative Hypothesis), as it is normally given to you in the problem - from Ha you can get the Ho (Null Hypothesis) by using the sign opposite to that found in the Ha.

A left 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 ____ - not be rejected since the p-value = 0.1212>0.10 - be rejected since the p-value = 0.1212>0.10 - not be rejected since the p-value = 0.0606<0.10 - be rejected since the p-value = 0.0606<0.10

- be rejected since the p-value = 0.0606<0.10 the p-value should always be rejected when it is less than α

when testing μ, 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 - optimistic - pessimistic - alternative

- null

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 I error - allowed probability of making a Type I error - observed probability of making a Type II error

- observed probability of making a Type I error

Suppose the competing hypotheses for a test are Ho: μ ≤ 33 versus Ha: μ > 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. - reject Ho, and conclude that the population mean is greater than 33 at the 5% significance level - do not reject Ho, and conclude that the population mean is greater than 33 at the 5% significance level - do not reject Ho and conclude that the population mean is not greater than 33 at the 5% significance level - reject Ho and conclude that the population mean is not greater than 33 at the 5% significance level

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

In hypothesis testing, two incorrect decision are possible - 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 - not rejecting the null hypothesis when it is false rejecting when true not rejecting when false

Steps to Hypothesis Testing

1. Determine the parameter of interest 2. Set up the hypothesis 3. Determine if a 1-tail or 2-tail test 4. Calculate test statistic 5. Choose p-value or critical value approach 6. Make decision whether or not to reject Ho

causation

A cause and effect relationship in which one variable controls the changes in another variable. we cannot test for causation

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

do not reject the null hypothesis when it is actually false

significance level

how much we allow ourselves to be wrong for a type 1 error

Ho

null hypothesis

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

null hypothesis is true

We can reject the null hypothesis when...

p-value < α

Make decisions whether or one to reject Ho

p-value approach (1) reject Ho if p-value < α, and accept Ha (2) do not reject Ho, if p-value ≥ α, and do not accept Ha (does not mean you accept Ho) critical value approach (1) reject Ho if |test statistic| > |critical value| can accept Ha (2) do not reject Ho |test statistic| < |critical value| - you can never prove the Ha or the Ho, you can only disprove or fail to disprove the Ho - the p-value will allow for a better interpretation of the rejection (or non rejection) of Ho

Choose p-value or critical value approach

p-value approach - calculate p-value from test statistic found in previous step critical value approach - calculate critical value from significance level (α)

null hypothesis

the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

regression

the idea of prediction and how one (or more) variable influences another variable

the basic principle of hypothesis testing is to assume that - the null hypothesis is false and see if the population data contradicts this assumption - the null hypothesis is true and see if the population data contradicts this assumption - the null hypothesis is false and see if the sample data contradicts this assumptions - the null hypothesis is true and see if the sample data contradicts this assumptions

the null hypothesis is true and see if the sample data contradicts this assumptions

Signs in Ha (alternative hypothesis)

the only signs that can be used in the Ha are (<) (>) (≠)

correlation

the strength of association/relationship between two quantitative variables gives us a positive or negative relationship a standardized value ranging from -1 to 1, where a value of 0 means there is no correlation between two variable -1: strong negative +1: strong positive

Determine the parameter of interest

the subject you are interested in testing

True or False A simple regression equation estimates a simple regression model

true

simple regression

we can make predictions of a response variable (factor) given the value of ONE explanatory variable

We do NOT reject the null hypothesis when the p-value is - < α - ≤ μ - > μ - ≥ α

≥ α

Signs in Ho (null hypothesis)

(≥) (≤) (=)

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

- sample, population

Determine if a 1-tail or 2-tail test

Determined by the sign 1-Tail Test - (<) left-tail - (>) right-tail 2-Tail Test - (≠)

True or False: A Type I error occurs if we do NOT reject the null hypothesis when it is actually false.

False

Calculate Test Statistic

If σ is known: z-test If σ is unknown: t-test If proportion: z-test (different formula)

alternative hypothesis

The hypothesis that states there is a difference between two or more sets of data. a claim or assertion for some outcome

True or False: In a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter

True

True or False: we choose a value for α before conducting a hypothesis test

True The value of α is decided prior to the hypothesis test

multiple regression

a prediction of a response variable given a value of more than one

p-value

a statement about the sample data in the context of Ho the probability of getting a sample statistic given the Ho is true the smaller the p-value, the stronger the evidence in your sample data again the Ho being true

Ha

alternative hypothesis in order to accept the Ha, the Ho has to be disproved (rejecting Ho) have to consider the probability of incorrectly rejecting the Ho

sample correlation (rxy)

attempts to estimate a correlation population parameter, pxy

type I error

being wrong and incorrectly rejecting the Ho when it is actually true

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

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

The two equivalent methods to solve a hypothesis test are the - population mean approach - critical value approach - standard deviation approach - p value approach

critical value approach p-value approach