Ch.10, and 15-1

Which of the following best summarizes the process of selecting a significance level for a hypothesis test of the mean?

The investigator should select the significance level before setting up the decision rule and taking the sample data.

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. Reason: It is the probability associated with the z statistic.

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

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

Choose the statements that correctly reflect traditional usage of significance level in statistical research. Select all that apply.

-Quality control uses a 1% significance level. -Consumer research uses a 5% significance.

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 > 1.65 -Fail to reject H0 if z < 1.65

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.

1.90 z = 6.7−5.52/10/2√

Ch.15-1 Which of the following is the correct formula for the test statistic, z, in a test of proportion?

z = p−π√π(1−π)n

A one-tailed and a two-tailed test have different critical values at the same significance level. Match the critical values to the to the correct test. Instructions

z=1.96 or -1.96 Choice H0:μ = 0, H1:μ ≠ 0, α=0.05 z=-2.33 Choice H0:μ≥0, H1:μ<0, α=0.01 z=2.58 or -2.58 Choice H0:μ=0, H1:μ≠0, α=0.01 z=1.65 Choice H0:μ≤0, H1:μ>0, α=0.05

Which symbol that represents the level of significance?

α (alpha)

Which of the following represents the probability of failing to reject the null hypothesis when it is false?

β

Ch.15-1 The test statistic for a test of proportion is z = p−π√π(1−π)np-ππ(1-π)n. Match the symbols to their description.

π matches Choice population proportion p matches Choice sample proportion n matches Choice sample size

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.

Suppose you are conducting a test with α=0.10, which of the following are true? Select all that apply.

For H0: μ≥25, the lower tail should include a rejection region equal to 0.10. For H0: μ=25, both the upper and lower tails include a rejection region equal to 0.05.

A cereal manufacturer tests a sample of 50 boxes of cereal to see if the average weight per box is 14 ounces. Which of these would be a valid null or alternative hypothesis for the given scenario?

H0: μ = 14

Which one of the following sets of hypotheses requires the use of a two-tailed test?

H0: μ = 5.6, H1: μ ≠ 5.6

Which of the following statements of a test hypothesis uses the correct protocol for choosing a null hypotheses? Select all that apply.

H0: μ = 88 H0: μ ≥ 27

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

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

What is the last step in the six step Hypothesis testing procedure?

Interpret the result.

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: Ho: μ=80,000 H1: μ≠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

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 > -1.65 Reject H0 if z < -1.65

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 Reason: z = 27−30/6/20√

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.

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

Suppose you are conducting a test with α=0.10, which of the following are true? Select all that apply.

-For H0: μ=25, both the upper and lower tails include a rejection region equal to 0.05. - For H0: μ≥25, the lower tail should include a rejection region equal to 0.10.

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.

Which of the following are essential elements of hypothesis testing? Select all that apply.

-It makes use of sample data. -It uses probability theory to determine if a hypothesis is a reasonable statement.

Which of the following statements are valid descriptions of the alternate hypothesis? Select all that apply.

-It tells what you will conclude if you reject the null hypothesis. -It is written symbolically as H1.

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.

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

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

Select all statements that correctly describe the null hypothesis.

-We either "reject" or "fail to reject" it, we cannot say that we "accept it" or that it is "true". -It is developed for testing purposes.

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

-When the null hypothesis is rejected when it should not be rejected, there is always the chance if a Type I error. -When the null hypothesis is not rejected when it should have been rejected, there is always the chance if a Type II error.

The probability of rejecting a true null is know as which of the following? Select all that apply.

-α -Type I error

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

0.04 Reason: z = 2.06

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

0.07 Reason: z = 1.5

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.

0.20 Choice Some evidence against H0. 0.05 matches Choice Strong evidence against H0. 0.01 matches Choice Very strong evidence against H0. 0.001 matches Choice Extremely strong evidence against H0.

Although the p-value does not give us the probability that the null hypothesis is true, it does suggest the likelihood that it is true. Match the p-value to the strength of the case in favor or the null hypothesis.

0.20 matches Choice A good chance H0 is correct. 0.05 matches Choice A slight chance H0 is true. 0.01 matches Choice Very slight chance H0 is true. 0.001 matches Choice Extremely poor chance H0 is true.

Suppose a hypothesis test, using α = 0.05, is being conducted with the following null hypothesis: H0: μ = 2. Which one of the following confidence intervals would lead to rejecting the null hypothesis?

A 95% confidence interval of 3 to 4.

Which of the following is correct?

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

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.

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

A statement about a population parameter subject to verification. Reason: Or more importantly, subject to falsification.

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.

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.

Ch.15-1 A test of proportion can use either the binomial distribution or the normal approximation. What is the requirement for using the normal approximation?

Both nπ and n(1-π) are at least 5.

Ch.15-1 Which of the following is the correct criteria for using the normal approximation while doing a test of proportion?

Both nπ and n(1-π) are at least 5.

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

No error was made.

Suppose you are performing a hypothesis test with σ unknown, n=29, α=0.01, and the following hypotheses: H0: μ ≤ 24 H1: μ > 24 What is the decision rule?

Reject H0 if the test statistic is greater than 2.467.

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.

Suppose you are performing a hypothesis test with σ unknown, n=22, α=0.05, and the following hypotheses: H0: μ = 24 H1: μ ≠ 24 What is the decision rule?

Reject H0 if the test statistic is less than -2.080 or greater than 2.080.

A model of car claims mileage of 24 mpg. with σ = 4 mpg. A sample of 4 cars got an average of 20.5 mpg. Test H0: μ = 24 H1: μ ≠ 24 at the 10% significance level.

Reject the null hypothesis Reason: zc = -1.65 and z = -1.75

A paint manufacturer claims that a gallon of their paint will cover at least 1200 square feet of smooth wall with σ = 80 square feet. Thirty-six gallons of paint were tested and the average square feet covered was 1175. Conduct a hypothesis test using a 5% significance level for: H0: μ ≥ 1200 H1: μ < 1200

Reject the null hypothesis Reason: zc = -1.65 and z = -1.88

If the test statistic for a hypothesis test (H0: μ=25) is z = 2.05 and the critical value for 5% significance is zc = 1.96, what should our conclusion be?

Reject the null hypothesis and conclude the alternative is true.

Ch.15-1 The binomial assumptions must be met when testing a hypothesis about population proportions. Which one of the following is not one of these assumptions?

Sampling is done from a small population without replacement.

What is the "critical value" for a hypothesis test?

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

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

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

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

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 = 10 H1: μ ≠ 10

Fail to reject the null hypothesis Reason: zc = 2.58 and z = 2.19

Choose the statement that best explains the use of the sample standard deviation in tests of the mean where the population standard deviation is not known.

The sample standard deviation is used as an estimate for the population standard deviation.

Ch.15-1 Which one of the following is not one of the binomial assumptions that must be met when testing a hypothesis about population proportions?

The variable is the number of times an event occurs during an interval.

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=12 H1: μ≠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.