McGraw Hill Education Connect BOWERMAN 9E CONNECT COURSE

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

.01

Order the examples below beginning with the instance where we have the most convincing evidence that the null hypothesis is wrong and ending with the instance where we have the least evidence.

0.002,.027,0.27

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 p-value?

0.0228

Which of the following statements are true?

1 If the null hypothesis is rejected, the alternative hypothesis is accepted to be true.

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

1 Not rejecting the null hypothesis when it is true.2.Rejecting the null hypothesis when it is false.

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 are not decisions we make when 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

An auditor for a small business wants to test the assumption that the mean value of all accounts receivable differs from $550. What are the null and alternative hypotheses for this test?

H0: μ = 550 versus Ha: μ ≠ 550

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

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

Which of the following statements are true

The probability of committing a Type I error is denoted α.

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 we wish to test H0: μ = 100 versus Ha: μ < 100. What happens if you make a Type II error?

You decide μ = 100 when μ < 100

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 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.

alternative

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

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. Testing the claim at the 1% significance level, using the p-value rule we

do not reject the null hypothesis

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

false

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

no error

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

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

the p-value is less than α

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

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 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

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 x is significantly less 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 is significantly greater than 100

Suppose you are using a critical value approach to test H0: μ ≤ 100 versus Ha: μ > 100 and you decide to use α =.025. You should reject the null hypothesis if

z > 1.96

xx is z = -2.88. Which alternative hypothesis would this z value support?

μ < 0