STATS EXAM 2 HOMEWORKS

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

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

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

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? Multiple choice question.

It would be the null hypothesis

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}

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

True

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 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 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 or research

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

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

no error

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? Multiple choice question.

null

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

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

the p-value is less than α

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

Which of the following statements are true? 2

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

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

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

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

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

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

In hypothesis testing, what are the two correct decisions possible? Multiple select question.

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.

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.