Chapter 10
p-value
determining this results in a decision regarding H0 a very small p (like .0001) indicates there is little llikelihood of H0 being treu. a p of .2033 means that H0 is not rejected and there is little likelihood it's false.
Which of the following statements of a hypothesis test violates the protocol for choosing null and alternate hypotheses?
H1: u <= -2 H0 must have the equality (>=). H1 can use != or < or >
Which of the following are necessary when you want to do a test of the population mean but the population standard deviation is unknown? select all
-find the sample standard deviation and use it as an estimate for the population statndar deviation -the t-distribution is used in place of the z-distribution, assuming a normal population
INTERPRETING THE WEIGHT OF EVIDENCE AGAINST H0
If the p-value is less than (a) .10, we have some evidence that H0 is not true. (b) .05, we have strong evidence that H0 is not true. (c) .01, we have very strong evidence that H0 is not true. (d) .001, we have extremely strong evidence that H0 is not true.
The significance level refers to the total area under the distribution in the region of rejection. what happens to this area in a two-tailed test?
It is divided into two equal parts, each half as large, one under each tail
What is the 'critical value' for a hypothesis test?
The dividing point between rejecting and failing to reject the null hypothesis.
What is the p-value
The probability that a sample value would be as far or further from the expected value, given that the null hypothesis is true. it is the probability associated with the z statistic
One-tailed test
The rejection region is only in one tail of the curve. (right or upper tail of the curve)
For a hypothesis test of h0: u <=2.5, h1: u>2.5, where would the rejection regions be?
The upper tail
The probability of rejecting a true null is known as which of the following?
Type I error a
Which of the following is the probability of failing to reject a false null hypothesis? select all that apply
Type II error B
We wish to test h0: u>=30 and h1: u <30 at the .05 level of significance. which of these statements are correct? select all that apply
fail to reject h0 if z > -1.65 reject h0 if z <-1.65
Match the level of significance to the type of research for which is is traditionally chosen
.05 consumer research .01 quality assurance .10 Political polling
A one-tailed and a two-tailed test have different critical values at the same significance level. Match the critical values to the correct test
z=+-1.96 :H0: u = 0, h1: u != 0, a=.05 z= -2.33 : H0: u >=0, h1: u <0, a = .01 z= +-2.58 : H0: u=0, h1 u!=0, a = .01 z= 1.65 : h0: u <=0, h1: u>0, a = .05
Which of the following is a "hypothesis" in a statistical sense? Select all that apply.
- The population mean lifetime of a particular brand of light bulb is at least 1000 hours -The population mean miles per gallon of a particular car is 44
Why do many statisticians prefer the use of "fail to reject the null hypothesis" instead of "accept the null hypothesis"? choose all that apply
- because hypothesis testing does not seek to prove the null -the null is assumed true to begin with
HYPOTHESIS TESTING
A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement. this used by statisticians does not provide proof that something is true. It provides a "proof beyond a reasonable doubt" in the court system. it has rules of evidence, or procedures.
Choose the best definition of "hypothesis" in the context of statistical analysis
A statement about a population parameter subject to verification
HYPOTHESIS
A statement about a population parameter subject to verification
which of the following is the best definition of the null hypothesis, h0?
A statement about a population parameter to be tested using sample measures
Null Hypothesis
A statement about a population parameter to be tested using sample measures. We either reject or fail to reject this. It's a statement that is not rejected unless our sample data provide convincing evidence that it's false.
In the context of hypothesis testing, what is a test statistic?
A value, determined from sample information, used to test the null hypothesis
A tire manufacturer claims its new tire has an average tread life of 80,000. To test to see if the process is true, the company conducts a hypothesis test using the following hypotheses: H0: u=80,000 H1: u !=80,000 Which of the following is the result of a Type II error?
Concluding the population average is 80,000 when it really isn't
IF the test statistic for a hypothesis test (H-: u=25) is z=2.05 and the critical value for 5% significance is z(ofc)=1.96 (critical value), what should our conclusion be?
Reject the null hypothesis and conclude the alternative is true
6 Steps that systematizes hypothesis testing
Step 1: State null and alternate hypothesis Step 2: Select a level significance Step 3: Identify the test statistic Step 4: Formulate a decision rule Step 5: Take a sample, arrive at decision Step 6: Interpret the result
which of the following best summarizes the process of selecting a significance level tor a hypothesis test of the mean?
The investigator should select the significance level before setting up the decision rule and taking the sample data
A tire manufacturer claims its new tire has an average tread life of 80,000. To test to see if the process is true, the company conducts a hypothesis test using the following hypotheses: H0: u=80,000 H1: u !=80,000 If the null is rejected, what would the interpretation be?
The manufacturer's claim is not true - the population average is not 80,000
LEVEL OF SIGNIFICANCE
The probability of rejecting the null hypothesis when it is true.
What is the meaning of 'level of significance' in the context of hypothesis testing?
The probability of rejecting the null hypothesis when it is true.
A soda bottling company fills bottles with 12 ounces of soda. overfilling causes the company to give away free soda. underfilling causes the company to cheat the customer. to test to see if the process is working correctly, the company conducts a hypothesis test using the following hypotheses: H0: u=12 H1: u != 12 If we fail to reject the null, what would the interpretation be?
There is insufficient evidence to conclude that the mean is different from 12
What is a confidence interval?
a range of values within which we expect the population parameter to occur.
For a hypothesis test of h0: u >=2.5, h1: u <2.5, where would the rejection regions be?
lower tail
Which of these formulas would you use to calculate the test statistic for a test of the mean with the population statndard deviation unknown?
t= xbar - u ----------- s/sqrt(n)
When testing a mean, where the population standard deviation is known, we calculate the test statistic using the formula z= (xbar-u)/(o/sqrt(n))
z = the test statistic xbar = the sample mean u = the population mean o/sqrt(n) = the standard error
Select all statements that correctly describe the null hypothesis
-it is developed for testing purposes -we either 'reject' or 'fail to reject' it, we cannot say that we 'accept it' or that it is 'true'
From the statements below, select all that are accurate descriptions of the null hypothesis
-the term 'null' referes to no significant difference -the null hypothesis is designated H0 -the purpose of the test is to prove the null hypothesis is false
Which of the following are true regarding estimation and hypothesis testing?
Both are statistical inference techniques
Alternate Hypothesis
a statement accepted if the sample data provide us with enough statistical evidence that the null hypothesis is false. Describes what you will conclude if you reject the null hypothesis. Written 'H1' and is read 'h sub one'. also referred to as the research hypothesis.
A soda bottling company fills bottles with 12 ounces of soda. overfilling causes the company to give away free soda. underfilling causes the company to cheat the customer. to test to see if the process is working correctly, the company conducts a hypothesis test using the following hypotheses: H0: u=12 H1: u != 12 Which of the following is the result of a Type I error?
Concluding the population average is not 12 when it really is
IF the test statistic for a hypothesis test (H0: u=11) is z=1.82 and the critical value for 5% significance is z=1.96 (critical value), what should our conclusion be?
Fail to reject the null
suppose you are conducting a test with a=.10, which ones of the following are true? select all that apply
for h0: u=25, both the upper and lower tails include a rejection region equal to .05 for h0: u >=25, the lower tail shoujld include a rejection region equal to .10
calculate the test statistic z for a population mean of 5.5, a population statndard deviation of 2, a sample mean of 6.7 and a sample size of 10
z = 1. 90 6.7-5.5 -------- 2/sqrt(10)