BA 2120 - LS 10

A camping tent is designed to be lightweight and to remain waterproof for at least five years. Let μ represent the mean number of years the tent remains waterproof. If the manufacturer has made the tent for some time and purchasers have been consistently impressed by its waterproofing, what role would the statement μ≥5 play in a test about μ?

It would be the null hypothesis

A new airline advertises that its customers will wait at most 30 minutes if a delay should happen. Let μ represent the mean number of minutes the customer waits in the event of a delay. If the airline has been in business for some time and its customers have been consistently impressed by their low short wait time when delays occurs, what role would the statement μ≤30 play in a test about μ?

It would be the null hypothesis

A drug company has developed a new form of insulin intended to keep blood sugar at healthy levels for longer periods than drugs currently on the market. The claim that the new insulin is superior to current drugs is

a research hypothesis

The ______ hypothesis, denoted Ha, is the statement that will be accepted only if there is convincing sample evidence that it is true.

alternatice

If we reject the null hypothesis when it is actually false we have committed ______.

no error

The ______ hypothesis, denoted H0, is the statement given the benefit of the doubt.

null

A Type I error occurs when we reject a null hypothesis that is ______.

true

A company has switched caterers for its cafeteria. To investigate whether prices have changed on average, the company should use a ______ alternative hypothesis.

two-sided

Suppose you wish to test the null hypothesis μ ≤ 100 versus the alternative μ >100. Which situation would provide support for the alternative?

when x(bar) is significantly greater than 100

Suppose you wish to test the null hypothesis μ ≥ 100 versus the alternative μ <100. Which situation would provide support for the alternative?

when x(bar) is significantly less than 100

Suppose the consequences of a Type I error are very serious. Which of the following values would be the most reasonable for α?

.01

Which of the following decision we do not make in hypothesis testing?

Accept the null hypothesis

A researcher for a store chain wants to determine whether the proportion of customers who try out the samples being offered is more than 0.15. What are the null and alternative hypotheses for this test?

H0: p ≤ 0.15 versus Ha: p > 0.15

Specify the competing hypotheses that would be used in order to determine whether the population mean differs from 15.

H0: μ = 15 versus Ha: μ ≠ 15

Specify the competing hypotheses that would be used in order to determine whether the population mean is less than 150.

H0: μ ≥ 150 versus Ha: μ < 150

Suppose an office manager hopes to establish that a new electronic reporting system decreases the time employees spend filling out travel forms. If they spent an average of 20 minutes filling out travel forms in the past, what hypotheses should the manager test?

H0: μ ≥ 20; Ha: μ < 20

In hypothesis testing, what are the two correct decisions possible?

Rejecting the null hypothesis when it is false. Not rejecting the null hypothesis when it is true.

In hypothesis testing, what are the two incorrect decisions possible?

Rejecting the null hypothesis when it is true. Not rejecting the null hypothesis when it is false.

Which of the following statements are true?

The null hypothesis and the alternative hypothesis are opposites of each other. If the null hypothesis is rejected, the alternative hypothesis is accepted to be true.

True or false: For a given sample size n, the chances of a Type I error can only be reduced at the expense of a higher chance of Type II error.

True

Under what circumstances do we reject a null hypothesis?

When the data make a strong case that it is incorrect.

Suppose we are testing H0: μ = 10 versus Ha: μ ≠ 10. When does a Type I error occur?

When we decide μ ≠ 10 when it is actually = 10.

Suppose you are bitten by a strange dog and don't know if the dog has rabies. Your null hypothesis is that the dog has rabies and therefore you should get a rabies shot; your alternative hypothesis is that the dog does not have rabies and therefore you should skip the shot. What happens to you if you make a Type II error?

You get a painful shot you don't really need.

Suppose you are very thirsty and you see a stream. You don't know whether it is safe to drink the water. Let your null hypothesis be that the water is not safe to drink and the alternative be that it is safe. What happens to you if you make a Type I error in this case?

You get sick from drinking unsafe water.

A car manufacturing company has developed a new tire to endure road wear for longer periods than tires currently on the market. The claim that the new tire is superior to current tires is

a research hypothesis

A Type II error occurs when we do not reject a null hypothesis that is ______.

false

Suppose that you wish to test H0: μ ≥ 0 and you find that the z statistic associated with x(bar) is z = -2.88. Which alternative hypothesis would this z value support?

μ < 0

Suppose you hope to establish that a population mean exceeds 100. You should use H0: μ ___ 100 and Ha: μ ___ 100.

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