Question

In: Statistics and Probability

In each of the following scenarios, tell if the researcher has committed a Type I error,...

In each of the following scenarios, tell if the researcher has committed a Type I error, a Type II error, or made a correct decision.

a.		A researcher is testing to determine if .31 of all families own more than one car. His null hypothesis is that the population proportion is .31. He randomly samples 600 families and obtains a sample proportion of .33 that own more than one car. Based on this sample data, his decision is to fail to reject the null hypothesis. The actual population proportion is .31.
b.		Suppose it is generally known that the average price per square foot for a home in a particular U.S. suburb is $73. A researcher believes that due to the economy, the average may now be less than that. To test her belief, she takes a random sample of 45 homes in this community, resulting in a sample mean of $70 per square foot. The researcher’s decision based on this sample information is to fail to reject the null hypothesis. The actual average price per square foot is now $68.
c.		Suppose a utility researcher knows from past experience that the average water bill for a 2000-square-foot home in a large Midwest city is $25 per month. The utility researcher wants to test to determine if this figure is still true today. Her null hypothesis is that the population mean is $25. To test this, she randomly samples 63 homes, resulting in a sample mean of $29. From this, she decides to reject the null hypothesis. The actual average is $27.
d.		According to PR Newswire, 71% of all expectant mothers wish they had to go to only one source to get their baby information. Suppose in your region of the country, you think that this figure is too high so you conduct a test of 358 expectant mothers. In your study, only 66% of the expectant mothers wish they had to go to only one source to get their baby information. Based on this, your decision is to reject the null hypothesis. It turns out that in actuality, 71% of all expectant mothers in your region of the country wish they had to go to only one source to get their information.

a.		Type II ErrorCorrect DecisionType I Error
b.		Correct DecisionType II ErrorType I Error
c.		Correct DecisionType I ErrorType II Error
d.		Type I ErrorType II ErrorCorrect Decision

Expert Solution

Type I error, a Type II error

type I error: When we reject the Null hypothesis but actually the null hypothesis is true.

Type II error: When we do not reject Ho but actually the Null hypothesis is false.

1)

A researcher is testing to determine if .31 of all families own more than one car. His null hypothesis is that the population proportion is .31. He randomly samples 600 families and obtains a sample proportion of .33 that own more than one car. Based on this sample data, his decision is to fail to reject the null hypothesis. The actual population proportion is .31.

His null hypothesis is that the population proportion is .31.

The actual population proportion is .31.

So here we can conclude that the null is true.

his decision is to fail to reject the null hypothesis.

So the decision also null is true.

So made the correct decision.

Answer:- made a correct decision

b)

Suppose it is generally known that the average price per square foot for a home in a particular U.S. suburb is $73. A researcher believes that due to the economy, the average may now be less than that. To test her belief, she takes a random sample of 45 homes in this community, resulting in a sample mean of $70 per square foot. The researcher’s decision based on this sample information is to fail to reject the null hypothesis. The actual average price per square foot is now $68.

the null hypothesis is the average price per square foot for a home in a particular U.S. suburb is $73.

The alternative hypothesis is the average price per square foot for a home in a particular U.S. suburb is less than .$73

The actual average price per square foot is now $68.

So it is less than 73.

So we should reject Ho.

Decision: fail to reject the null hypothesis.

So we have made an error.

we do not reject Ho but actually the Null hypothesis is false.

So it is type II error.

Answer:- Type II error.

c) Suppose a utility researcher knows from past experience that the average water bill for a 2000-square-foot home in a large Midwest city is $25 per month. The utility researcher wants to test to determine if this figure is still true today. Her null hypothesis is that the population mean is $25. To test this, she randomly samples 63 homes, resulting in a sample mean of $29. From this, she decides to reject the null hypothesis. The actual average is $27.

Her null hypothesis is that the population mean is $25.

The actual average is $27. which is not equal to $ 25.

So we should reject the null hypothesis.

Decision: Reject the null hypothesis

We made the correct decision

Answer:- Made correct Decision.

d)

According to PR Newswire, 71% of all expectant mothers wish they had to go to only one source to get their baby information. Suppose in your region of the country, you think that this figure is too high so you conduct a test of 358 expectant mothers. In your study, only 66% of the expectant mothers wish they had to go to only one source to get their baby information. Based on this, your decision is to reject the null hypothesis. It turns out that in actuality, 71% of all expectant mothers in your region of the country wish they had to go to only one source to get their information.

The null hypothesis is 71% of all expectant mothers wish they had to go to only one source to get their baby information.

actuality, 71% of all expectant mothers in your region of the country wish they had to go to only one source to get their information.

So we should not reject Ho.

Decision made:- reject the null hypothesis

Made an error

we reject the Null hypothesis but actually the null hypothesis is true.

So we made type I error.

Answer:- Type I error.

orchestra answered 2 years ago

For each of the scenarios below, select whether a correct decision, a type I error, or...

For each of the scenarios below, select whether a correct decision, a type I error, or a type II error was made. 1- A marketing manager determines that an increase in expenditure for a particular stream of social-media marketing will not result in an increase in the number of customers reached by that stream. After increasing the expenditure, the manager installs a tracking app that confirms the number of customers reached has not increased. 2-Looking at the results of an...

7. Below are research scenarios. For each, indicate whether the researcher committee a Type 1 error,...

7. Below are research scenarios. For each, indicate whether the researcher committee a Type 1 error, a Type 2 error, or no error in hypothesis testing (a) Assume there is a strong, positive relationship between variable X (number of hours per week a child reads for pleasure) and variable Y (language arts scores in the classroom) in the population of 3rd grade students in the United States. As with any educational study, researchers investigating the relationship between X and Y...

Suppose a researcher wants to make sure that the probability of committing a Type I error...

Suppose a researcher wants to make sure that the probability of committing a Type I error is less than 5%. How can the researcher control for this? Set the value for a Type II error at 0.05. Set the alpha level at 0.05. Place the rejection region in both tails. Both setting the alpha level at 0.05 and placing the rejection region in both tails.

Describe and tell me the difference between a Type 1 and Type 2 error. Which error...

Describe and tell me the difference between a Type 1 and Type 2 error. Which error is directly related to your alpha? Which error is also called your beta? When your answer is more conservative, does your error rate go up or down? Give an example of two alphas and tell me which one is the more conservative choice.

I. In each of the following two scenarios, what type of transaction is involved? (spot exchange,...

I. In each of the following two scenarios, what type of transaction is involved? (spot exchange, contract, or vertical integration). Explain your answer. 3. XYZ Corporation a big automobile company purchases Mich Tires, a local tire company. 4. Each year LAREDO bell, a new fast food company, has a legal obligation to purchase 0.5 billion pounds of potatoes from AGRI Expert located in San Antonio.

How is statistical power related to the following concepts: Type I error, Type II error, variance,...

How is statistical power related to the following concepts: Type I error, Type II error, variance, effect size, and sample size.

What is a Type I Error? What is the impact on Type II Error if we...

What is a Type I Error? What is the impact on Type II Error if we reduce the likelihood of Type I Error? Please upload in Microsoft Word.

2.3. Each of the following scenarios presents a claim by a researcher. Assume that the sample...

2.3. Each of the following scenarios presents a claim by a researcher. Assume that the sample sizes in each case was in the range of 20 to 25 observations per sample in each case. Answer the following for each scenario: (i) state the appropriate null (HO) and alternate hypothesis (HA) in symbolic form (e.g. Hx : Meanleft = Meanright); (ii) indicate whether it is a 1or 2-tailed test, and if a 1-tailed tests which tail is the area of rejection...

Provide one example each of both a Type I and Type II error that could occur...

Provide one example each of both a Type I and Type II error that could occur when running predictive engines relevant to sports betting. Which is likely to be more costly and why?

Describe what would be a type I error and what would be a type II error:...

Describe what would be a type I error and what would be a type II error: A restaurant claims more than 42% of its new patrons return at least once within a month.