Significance Test for Means

A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers does not believe this is so. They take a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000. What set of hypotheses are they interested in testing?

• a) H₀: μ = 50,000 vs. Ha: μ < 50,000

• b)H₀: x̅ = 50,000 vs. Ha: x̅ < 50,000

• c)H₀: μ = 50,000 vs. Ha: μ ≠ 50,000

• d)H₀: μ = 50,000 vs. Ha: μ > 50,000

A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers does not believe this is so. They took a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000. If 0.0100 < P-value < 0.0200, what decision should be made if testing at the α = 0.05 level?

• a)Reject H₀ and conclude that the tires were not performing as claimed.

• b)Reject H₀ and conclude that the mean tire life really is 50,000 miles.

• c)Do not reject H₀ and conclude that the tires were not performing as claimed.

• d)Do not reject H₀ and conclude that the mean tire life really is 50,000 miles.

Another word for average is

• sample 
• mean
• data
• numerical data

A hypothesis always describes a

• Sample

• Standard Error

• proportion

• Population

In performing a hypothesis test where the null

hypothesis is that the μ = 6.9, a random sample of 16

items is selected. The sample mean is 7.1 and the sample

standard deviation is 2.4. It can be assumed that the

population is normally distributed and there are no outliers. At α = .05 we can conclude

• There is enough evidence to reject the claim

• There is not enough evidence to reject the claim

• There is enough evidence to support the claim

• There is not enough evidence to support the claim

The average miles on a tank of gas for the Ford

Explorer is 300 miles. A consumer group feels the average is actually lower. They survey 40 vehicles and find the average

miles per tank is 290 miles, and the standard deviation is 22. At α = 0.01, is there evidence to support the consumer group's concern?

• There is enough evidence to reject the claim

• There is not enough evidence to reject the claim

• There is enough evidence to support the claim

• There is not enough evidence to support the claim

In performing a hypothesis test where the null

hypothesis is that the μ = 6.9. A random sample of 16

items is selected. The sample mean is 7.1 and the sample

standard deviation is 2.4. It can be assumed that the

population is normally distributed at α = .05.

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

A nutritionist claims U.S. children drink an average of less than 2 glasses of milk per day. Based on an SRS of 30 children, the p-value of H₀: μ = 2 vs. H_A: μ < 2 is 0.0015. What is the correct interpretation of the p-value?

• The probability that she fails to reject the null hypothesis is 0.015%

• The probability that she rejects the null is 0.015%

• She can be 99.85% confident that the alternative hypothesis is true

• About 0.15% of all samples would produce a test statistics at least as extreme as ours if the null hypothesis is true.

• About 99.85% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.

You are testing a new medication and believe that making a type 1 error could cause serious harm. You should set the significance level of the test to be

• .20

• .10

• .05

• .01

When setting up a significance test, you believe that the consequences for a type 2 error are much greater than for a type 1 error. Which significance level should you use?

• .10

• .05

• .01

• It does not matter