Chapter 10

which of the following statements accurately describe the alternate hypothesis

- it is also called the research hypothesis -it is accepted as a consequence of the null hypothesis being rejected

Calculate the test statistic z for a population mean of 30, a population standard deviation of 6, a sample mean of 27 and a sample size of 20.

-2.24 (27−30)/(6/√20)

Why do many statisticians prefer the use of "fail to reject the null hypothesis" instead of "accept the null hypothesis"? Select all that apply.

-because the null is assumed true to begin with -because hypothesis testing does not seeking to prove the null

Find the p-value (to two significant digits) for the following test.H0: μ = 0, H1: μ ≠ 0, σ = 1, z = 2.06Hint: the population follows the standard normal distribution.

0.0394 0.5-0.4803=0.0197 0.0197&*2=0.0394

Match the level of significance to the type of research for which it is traditionally chosen.

0.05= consumer research 0.01=quality assurance 0.10=political polling

Find the p-value (to two significant digits) for the following test.H0: μ ≤ 0, H1: μ > 0, σ = 1, z = 1.5Hint: the population follows the standard normal distribution.

0.0668

Which of the following is correct?

A 99% confidence interval can be used to conduct a two-tailed test with α=0.01.

Which of the following are true regarding estimation and hypothesis testing?

Both are statistical interference techniques.

Choose the two statements that correctly reflect traditional usage of significance level in statistical research.

Consumer researchers use a 5% significance. Quality Control uses a 1% significance level.

If the test statistic for a hypothesis test (H0: μ=11) is z = 1.82 and the critical value for 5% significance is zc = 1.96, what should our conclusion be?

Fail to reject the null.

Which of the following statements of a test hypothesis violates the protocol for choosing null and alternate hypotheses?

H1: μ ≤ -2

If we reject a false null hypothesis, what type of error would we be making?

No error was made.

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: Ho: μ=12H1: μ≠12If we fail to reject the null, what would the interpretation be?

There is insufficient evidence to conclude that the mean is different from 12.

which one of the following best describes hypothesis testing?

a procedure based on sample evidence and probability to see if a hypothesis is a reasonable statement

in the context of hypothesis testing, what is a test statistic?

a value, determined from a sample information, used to test the null hypothesis

in the context of hypothesis testing, what is a test statistics?

a value, determined from sample information, used to test the null hypothesis.

suppose you are performing a hypothesis test with o unknown, n=25, and the following hypotheses: H0:u>/>100 H1:u<100 If the test statistics was -1.440. what would the p value be?

between 0.05 and 0.10

for a hypothesis test of Ho:u=2.7; H1:u=/=2.7 where would the rejection regions be?

both tails

Calculate the test statistic z for a population mean of 5.5, a population standard deviation of 2, a sample mean of 6.7 and a sample size of 10.

z = 1. 90

Knowing the p-value allows us to asses the weight of evidence against the null hypothesis. Match the p-value to the relative strength of evidence.

0.2= some evidence against H0 0.05=strong evidence against h0 0.01=very strong evidence against H0 0.001=extremely strong evidence against H0

Hypothesis testing follows a six step procedure. Place these steps in order (first at the top).

1. State null and alternate hypothesis 2. Select a level of significance 3. Identify the test statistic 4. Formulate a decision rule 5. Take a sample and make a decision 6. Interpret the result

Choose the best definition of "hypothesis" in the context of statistical analysis.

A statement about a population parameter subject to verification.

Choose the best definition of the Alternate Hypothesis, H1?

A statement that is accepted if there is significant evidence that the null hypothesis is false.

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: Ho: μ=12H1: μ≠12Which of the following is the result of a Type I error? Concluding the population average is not 12 when it really is. Match the

Concluding the population average is not 12 when it really is.

We wish to test H0: μ ≥ 30 and H1: μ < 30 at the 0.05 level of significance. Which of these statements are correct? Select all that apply.

Fail to reject H0 if z > -1.65Reject H0 if z < -1.65

A brand of chocolate bar has a stated weight of 6 oz. with σ = 0.25 oz. A sample of 9 bars has an average weight of 6.05 oz.Test H0: μ = 6 oz. H1: μ ≠6 oz. at the 5% significance level.

Fail to reject the null hypothesis Reason: zc = 1.96 and z =(6.05-6)/(0.25/ square root 9)= 0.6

A bag of potatoes has a stated weight of 10 pounds with σ = 0.75 pound. A sample of 30 bags has an average weight of 10.3 pounds. Conduct a hypothesis test using a 1% significance level for: H0: μ = 10H1: μ ≠ 10

Fail to reject the null hypothesis xc=2.58 and z=2.19

Which of the following sets of hypotheses require the use of a one-tailed test? Select all that apply.

H0: μ ≤ -25, H1: μ > -25H0: μ ≥ 7.5, H1: μ < 7.5

Which of the following statements accurately describe the p-value? Select all that apply.

If we reject the null, it is the probability of making a Type I error. The null is rejected when the p-value is less than α.

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.

which of the following are essential elements of hypothesis testing?

It makes use of sample data. It uses probability theory to determine if a hypothesis is a reasonable statement. It is based on data collected from a sample.

Suppose you are performing a hypothesis test with σ unknown, n=23, α=0.10, and the following hypotheses: H0: μ ≥ 24 H1: μ < 24 What is the decision rule?

Reject H0 if the test statistic is less than -1.321.

We wish to test H0: μ ≤ 12 and H1: μ > 12 at the 0.05 level of significance. Which of these statements are correct? Select all that apply.

Reject H0 if z > 1.65Fail to reject H0 if z < 1.65

Which of the following is a "hypothesis" in the 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.

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.

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.

What is a "decision rule" in the context of hypothesis testing?

The specific conditions under which the null hypothesis is to be rejected.

What is the correct procedure when you want to do a test of the population mean but the population standard deviation is unknown? Select all that apply.

The t-distribution is used in place of the z-distribution, assuming a normal population. Find the sample standard deviation and use it as an estimate for the population standard deviation.

From the statements below, select all that are accurate descriptions of the null hypothesis.

The term "null" refers to no significant difference. The null hypothesis is designated H0. The purpose of the test is to prove the null hypothesis is false.

when testing a mean, where the population standard deviation is known, we calculate the test statistic using the formula z= (X-u)/ (o/square root n). Which one of the following is accurate with regarding statistics?

The test statistics measures the difference between the statistic the vale of parameter in the null.

which of the following statements of a test hypothesis violates the protocol for choosing null and alternate hypotheses?

h0:u>32 explanation= the null hypothesis always contains the equality (>,< or =) Null refers to it being the hypothesis of no difference. H1:u<30 explanation= H0 must have the equality (<). H1 can use =/= or < or >.

Which one of these formulas would you use to calculate the test statistic for a test of the mean with the population standard deviation unknown?

t= (x-u)/(s/ Square root n)

which of the following is true about p-value

the closer the p value is to 0 the more evidence to reject the null

what is the critical value for hypothesis test?

the dividing point between rejecting and failing to reject the null hypothesis.

when testing a mean, where the population standard deviation is known, we calculate the test statistic using the formula z= (X-u)/ (o/square root n)

z- the test statistics x- the sample mean - u- the population mean o/ square root n- the standard error