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

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