Question

For Problems 5-8: For each of the statements:

5. The mean amount of credit card debts per adult in the US is greater than $3,500.

The hypotheses statements: Ho: μ ≤ 3500 vs H1: μ > 3500 (claim)

Give a statement identifying a Type I Error.

Choose your correct answer below.

A) The amount of credit card debt is equal to $3500.

B) The amount of credit card debt is less than $3500.

C) The amount of credit card debt is greater than $3500.

D) The amount of credit card debt is not equal to $3500.

6. WHO Air quality guideline for particulate matter (PM1O) is 50 micrograms/cubic meter. That is, 50 is the mean value.

Hypotheses statements: Ho: μ = 50 (claim) vs H1: μ ≠ 50. Give a statement identifying a Type I Error.
Choose the correct answer below.

A) WHO Air quality guideline for particulate matter (PM1O) is equal 50 micrograms/cubic meter.

B) WHO Air quality guideline for particulate matter (PM1O) is less than 50 micrograms/cubic meter.

C) WHO Air quality guideline for particulate matter (PM1O) is greater than 50 micrograms/cubic meter.

D) WHO Air quality guideline for particulate matter (PM1O) is not 50 micrograms/cubic meter.

7. The mean of the weekly work hours for a country is less than 34 hours.

Hypotheses statements: Ho: μ ≥ 34 vs H1: μ< 34. (claim)

Give a statement identifying a Type II Error.

Choose the correct answer below.

A) The mean of the weekly work hours for the country is equal to 34 hours.

B) The mean of the weekly work hours for the country is less than to 34 hours.

C) The mean of the weekly work hours for the country is greater than to 34 hours.

D) The mean of the weekly work hours for the country is not equal to 34 hours.

8. The graduation rate at CASA magnet school is 90%.

Hypotheses statements: Ho: p = 0.90 (claim) vs H1: p ≠0.90

Give a statement identifying a Type II Error.

Choose the correct answer below.

A) The graduation rate at CASA magnet school is equal to 90%.

B) The graduation rate at CASA magnet school is less than 90%.

C) The graduation rate at CASA magnet school is greater than 90%.

D) The graduation rate at CASA magnet school is not equal to 90%.

Answer 1

Hello Sir/ Mam

Type I error occurs when we do not have sufficient evidence to reject the null hypothesis, but we still reject the null.

Type II error occurs when we have sufficient evidence to reject the null hypothesis, but we still don't reject the null.

Hence,

(a) THE CORRECT ANSWER IS OPTION C : The amount of credit card debt is greater than $3500

Type I error means that we can't reject the null but we still have.

Rejecting the null means that the amount of credit card debt is greater than $3500.

(b) THE CORRECT ANSWER IS OPTION D : WHO Air quality guideline for particulate matter (PM1O) is not 50 micrograms/cubic meter.

Type I error means that we can't reject the null but we still have.

Rejecting the null means that WHO Air quality guideline for particulate matter (PM1O) is not 50 micrograms/cubic meter.

(c) THE CORRECT ANSWER IS OPTION C : The mean of the weekly work hours for the country is greater than or equal to 34 hours.

Type II error occurs when we should reject the null, but we don't.

Not rejecting the null means the mean of the weekly work hours for the country is greater than or equal to 34 hours.

(d) THE CORRECT ANSWER IS OPTION A : The graduation rate at CASA magnet school is equal to 90%.

Type II error occurs when we should reject the null, but we don't.

Not rejecting the null means accepting that the graduation rate at CASA magnet school is equal to 90%.

I hope this solves your doubt.

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