SB 10.1-10.2. 10.4

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

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

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

Suppose we are testing H0: μ ≤ 20 versus Ha: μ > 20. If the test statistic is Z = 1.88, the p-value is

P{z ≥ 1.88}

Suppose the competing hypotheses for a test are H0: μ ≤ 10 versus Ha: μ >10. If the p-value is 0.0139 and the level of significance is 5%, what is the correct conclusion?

Reject H0

Suppose the competing hypotheses for a test are H0: μ ≤ 10 versus Ha: μ >10. If the value of the test statistic is 2.50 and the critical value at the 5% level of significance is z0.05 = 1.645, what is the correct conclusion?

Reject H0

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 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

Suppose a company has developed a new glass to be used in cell phone screens. If the company claims the new glass can withstand more punishment than the glass in current use, then this claim should be made the _________ hypothesis and the statement that the glass really is no better than the current glass should be made the ________ hypothesis.

alternative; null

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

no error

Suppose that a firm manufacturing coffee urns has found that its urns dispense coffee at a mean temperature of 158° and that the actual temperatures are quite consistent. If we were to set up hypotheses to test whether the urns meet the specified target temperature of 158°, we should regard the hypothesis that μ =158 as

the null hypothesis

In a "greater than" hypothesis test, the null hypothesis is rejected if and only if ______.

the p-value is less than α

In a "greater than" hypothesis test, the null hypothesis is rejected if and only if ______.

the test statistic is greater than the critical value

In a "less than" hypothesis test, the null hypothesis is rejected if and only if ______.

the test statistic is less than the critical value

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 less than 100

Suppose that we want to test the claim that the mean of a population is greater than 20. Also suppose that the population standard deviation is known to be 7. A sample of 49 measurements reveals a mean of 22. What is the value of the test statistic? ______

2.00

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

Accept the null hypothesis

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

False

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 proportion is greater than 0.35.

H0: p ≤ 0.35 versus Ha: p > 0.35

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

An auditor for a small business wants to determine whether the mean value of all accounts receivable is less than $550. What are the null and alternative hypotheses for this test?

H0: μ ≥ 550 versus Ha: μ < 550

Which of the following statements are true?

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

Suppose the competing hypotheses for a test are H0: μ ≥ 10 versus Ha: μ < 10. If the value of the test statistic is -2.50 and the critical value at the 5% level of significance is -z0.05 = -1.645, what is the correct conclusion?

Reject H0

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.

Which of the following statements are true?

The probability of committing a Type I error is denoted α. α is usually set between 0.05 and 0.01 The probability of committing a Type II error is denoted β.

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

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

True or false: When calculating a p-value, we always assume that the null hypothesis is true.

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.

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

null

The p-value is defined as the probability ______.

of observing a test statistic that is at least as contradictory to the null hypothesis as the test statistic actually computed from a sample

The critical value of a "less than" hypothesis test is ______.

the point under the standard normal curve that gives a left hand tail area equal to α

The critical value of a "greater than" hypothesis test is ______.

the point under the standard normal curve that gives a right hand tail area equal to α

Suppose that you wish to test H0: μ ≥ 0 and you find that the z statistic associated with xx 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.

≤; >