Ch. 10 BUS Statistics

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.

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Which of the following statements of a test hypothesis uses the correct protocol for stating an alternate hypothesis? Select all that apply.

H1: μ ≠ 24 H1: μ < 30

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

β

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

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

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.

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

A statement about a population parameter subject to verification.

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 Which of the following is the result of a Type I error?

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

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

H0: μ ≥ 27 H0: μ = 88

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.

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

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

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

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

H0: μ ≤ -25, H1: μ > -25 H0: 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.

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.

The result of a hypothesis test was traditionally reported as either "reject H0" or "fail to reject H0". What is the purpose of reporting the p-value in addition?

It provides additional insight into the strength of the decision.

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.

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

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

Type I error α

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

The dividing point between rejecting and failing to reject 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: 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

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.

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

The formula that is used to find the statistic for a Type II error is z = Xc−μ1σ/√nXc-μ1σ/n Match the variable to its description.

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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

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

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.

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

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

To emphasize that there is always the possibility of a Type II error, which typically cannot be quantified. Because only by rejecting the null hypothesis can we calculate the probability of a Type I error.