stats 1 final chow

independent random samples

-completely independent of one another -we generally assume the twi sample means are derived from two independent normally distributed populations because a linear combination of of normally distributed random variables is also normally distributed

three steps when formulating the competing hypothesis

1. identify the relevant population parameter of interest 2. determine whether it is a one or two-tailed test 3. include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim

p-value approach

1. specify the null and alternative hypothesis 2. specify the test statistic and its compute value 3. calculate the p-value 4. state the conclusion and interpret results -likelihood of obtaining a sample mean that is at least as extreme as the one derived from the given sample, under the assumption that the null is true

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The value of the test statistic in this problem is approximately equal to

2.80

If we are testing for the difference between the means of 2 independent populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to

38

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

>or=a

alternative hypothesis

Ha-contradicts the default state or status quo. covers all possible values of the population parameter.

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 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 >or=550, Ha <550

null hypothesis

Ho- corresponding to a presumed default state of nature or status quo. covers all possible values of the population parameter.

In testing for differences between the means of two independent populations, the null hypothesis is:

Ho:u1-u2=0

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: x bar = 52, s = 22. Suppose the alternative we wanted to test was H1 :u < 60. State the correct rejection region for a = 0.05.

Reject Ho if t < -1.6604

We have created a 95% confidence interval for u with the result (10, 15). What decision will we make if we test Ho : u =16 vs H1 : u doesnot= 16 at a = 0.05?

Reject Ho in favor of H1

An entrepreneur is considering the purchase of a coin-operated laundry. The present owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals a daily average revenue of $625. If you were to test the null hypothesis that the daily average revenue was $675 and decide not to reject the null hypothesis, what can you conclude?

There is not enough evidence to conclude that the daily average revenue was not $675.

a type 1 error is commonly denoted as

a

statistical inference concerning the difference in population means is based on the condition that the sampling distribution of x bar 1 - x bar 2follows

a normal distribution

If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000

a one tailed test should be utilized

one-tailed hypothesis

a one-tailed test, on the other hand, involves a null hypothesis that can only be rejected on one size of the hypothesized value.

two-tailed hypothesis

a two-tailed test is defined when a null hypothesis states a specific value for the population parameter of interest. if the null hypothesis is rejected, it suggests that the true parameter does not equal the hypothesized value. can be rejected on either side.

which of the following is true

a= the probability of committing a type 1 error B= the probability of committing a type 2 error

if a researcher accepts a true null hypothesis she has made a

decision

if a researcher rejects a false null hypothesis she has made a

decision

if a researcher accepts a false null hypothesis she has made a

error

if a researcher directs a true null hypothesis, she has made a

error

for a given level of significance, if the sample size is increased, the probability of committing a type 1 error will increase

false

we use _____ tests to address conflicts between two competing views on a particular population parameter

hypothesis

two tailed test

if Z < 0, then p-value =2P(Z<or=z) if Z > 0, then p value = 2P(Z>or=z)

-

in statistics we use sample information to make inferences regarding the unknown population parameters of interest

two or more samples are _____ if the process that generated one sample is completely separate from the process that generated the other sample

independent

type 1 error

is committed when we reject the null hypothesis when the null hypothesis is actually true. denoted by a. as the sample size increases, both type 1 and type 2 tend to decrease.

type 2 error

is made when we do not reject the null hypothesis and the null hypothesis is actually false. denoted by B

In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are

n1+n2-2

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> or =1.55)= 00606. The null hypothesis should ______

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

the hypothesis denoted by the Ho, is the _____ hypothesis and the hypothesis denoted by the Ha is the ___

null, alternative

left tailed test

p value = P(Z<or=z) if Z is >or=0, then the null can never be rejected

right tailed test

p-value = P(Z>or=z) if Z is <or= 0, then the null can never be rejected

the decision rule (critical value)

reject null if z >za for a right tailed reject null if z < -za for a left tailed reject null if z > za/2 or z < -za/2 for a two tailed test

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

reject the null hypothesis

hypothesis testing

some form of the equality sign must appear in the null hypothesis -enables us to determine whether sample evidence is inconsistent with what is hypothesized under the null hypothesis

the critical value approach

specifies a region of values, also called the rejection region, such that if the test statistic falls within the rejected region, we reject the null. it separates the rejection region from the non rejection region

reject or not reject

the hypothesis testing procedure enables us to make one of two decisions. if sample evidence is inconsistent to the null hypothesis, we reject the null hypothesis. conversely, if sample evidence is consistent with the null hypothesis, we do not reject. its not correct to conclude "we accept the null hypothesis" because while the sample data might not be inconsistent with the null hypothesis, it does not necessarily prove that the null hypothesis is true.

if the p-value is less than a in a two tailed test,

the null hypothesis should be rejected

which of the following would be an appropriate null hypothesis?

the population proportion is no less than 0.65

the power of the test

the probability of rejecting the null hypothesis when the null hypothesis is false.since B is the probability of a Type 2 error, the power of the test is defined as 1-B

the decision rule

to reject the null hypothesis when the p-value <a and not reject when the p-value is > or =a

A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.05.

true

a type 2 error is committed when

we don't reject a null hypothesis that is false

a type 1 error is committed when

we reject a null hypothesis that is true

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?

z test of a population proportion