Questions: Describe type I and type II errors for a hypothesis test of the indicated claim. An urban planner claims that the noontime mean traffic flow rate on a busy downtown college campus street is at least 32 cars per minute. Describe the type I error. Choose the correct answer. A. A type I error will occur when the actual noontime mean traffic flow rate is no more than 32 cars per minute, but you fail to reject H0: μ ≤ 32. B. A type I error will occur when the actual noontime mean traffic flow rate is at least 32 cars per minute, but you fail to reject H0: μ ≥ 32. C. A type I error will occur when the actual noontime mean traffic flow rate is at least 32 cars per minute, but you reject H0: μ ≥ 32. D. A type I error will occur when the actual noontime mean traffic flow rate is no more than 32 cars per minute, but you reject H0: μ ≤ 32.

Describe type I and type II errors for a hypothesis test of the indicated claim. An urban planner claims that the noontime mean traffic flow rate on a busy downtown college campus street is at least 32 cars per minute.

Describe the type I error. Choose the correct answer. A. A type I error will occur when the actual noontime mean traffic flow rate is no more than 32 cars per minute, but you fail to reject H0: μ ≤ 32. B. A type I error will occur when the actual noontime mean traffic flow rate is at least 32 cars per minute, but you fail to reject H0: μ ≥ 32. C. A type I error will occur when the actual noontime mean traffic flow rate is at least 32 cars per minute, but you reject H0: μ ≥ 32. D. A type I error will occur when the actual noontime mean traffic flow rate is no more than 32 cars per minute, but you reject H0: μ ≤ 32.

Transcript text: Describe type I and type II errors for a hypothesis test of the indicated claim. An urban planner claims that the noontime mean traffic flow rate on a busy downtown college campus street is at least 32 cars per minute. Describe the type I error. Choose the correct answer. A. A type I error will occur when the actual noontime mean traffic flow rate is no more than 32 cars per minute, but you fail to reject $\mathrm{H}_{0}: \mu \leq 32$. B. A type I error will occur when the actual noontime mean traffic flow rate is at least 32 cars per minute, but you fail to reject $\mathrm{H}_{0}: \mu \geq 32$. C. A type I error will occur when the actual noontime mean traffic flow rate is at least 32 cars per minute, but you reject $\mathrm{H}_{0}: \mu \geq 32$. D. A type I error will occur when the actual noontime mean traffic flow rate is no more than 32 cars per minute, but you reject $\mathrm{H}_{0}: \mu \leq 32$.

Solution

Solution Steps

Step 1: Define the Hypotheses

In this hypothesis test, we are evaluating the claim made by an urban planner regarding the noontime mean traffic flow rate on a busy downtown college campus street. The hypotheses are defined as follows:

Null Hypothesis ($H_0$): $\mu \geq 32$
Alternative Hypothesis ($H_a$): $\mu < 32$

Step 2: Understand Type I and Type II Errors

In the context of hypothesis testing:

A Type I error occurs when we reject the null hypothesis ($H_0$) when it is actually true.
A Type II error occurs when we fail to reject the null hypothesis when the alternative hypothesis ($H_a$) is true.

Step 3: Analyze the Options for Type I Error

We need to evaluate the provided options to identify the correct description of a Type I error:

Option A: A Type I error will occur when the actual noontime mean traffic flow rate is no more than 32 cars per minute, but you fail to reject $H_0: \mu \leq 32$.
This describes a Type II error.
Option B: A Type I error will occur when the actual noontime mean traffic flow rate is at least 32 cars per minute, but you fail to reject $H_0: \mu \geq 32$.
This describes a correct decision, not an error.
Option C: A Type I error will occur when the actual noontime mean traffic flow rate is at least 32 cars per minute, but you reject $H_0: \mu \geq 32$.
This correctly describes a Type I error.
Option D: A Type I error will occur when the actual noontime mean traffic flow rate is no more than 32 cars per minute, but you reject $H_0: \mu \leq 32$.
This describes a correct decision, not an error.