According to a report, the mean of monthly cell phone bills was $48.28 three years ago. A researcher suspects that the mean of monthly cell phone bills is less today. (a) Determine the null and alternative hypotheses. (b) Explain what it would mean to make a Type I error. (c) Explain what it would mean to make a Type Il error.

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**Hypothesis Testing for Mean Cell Phone Bills**

According to a report, the mean of monthly cell phone bills was $48.28 three years ago. A researcher suspects that the mean of monthly cell phone bills is less today.

**Steps Involved in Formulating Hypotheses and Understanding Errors:**

**(a) Determine the null and alternative hypotheses.**

- **Null Hypothesis (H₀):** The mean of monthly cell phone bills today is equal to $48.28.
- **Alternative Hypothesis (H₁):** The mean of monthly cell phone bills today is less than $48.28.
  
These hypotheses are represented visually as:

- H₀: [ = ] $48.28
- H₁: [ < ] $48.28

**(b) Explain what it would mean to make a Type I error.**

A Type I error occurs when the null hypothesis is true, but we mistakenly reject it. In this context, it means concluding that the mean monthly cell phone bill has decreased from $48.28 when, in reality, it has not.

**(c) Explain what it would mean to make a Type II error.**

A Type II error happens when the null hypothesis is false, but we fail to reject it. Here, it implies failing to recognize that the mean monthly cell phone bill is actually less than $48.28 when it has indeed decreased.
Transcribed Image Text:**Hypothesis Testing for Mean Cell Phone Bills** According to a report, the mean of monthly cell phone bills was $48.28 three years ago. A researcher suspects that the mean of monthly cell phone bills is less today. **Steps Involved in Formulating Hypotheses and Understanding Errors:** **(a) Determine the null and alternative hypotheses.** - **Null Hypothesis (H₀):** The mean of monthly cell phone bills today is equal to $48.28. - **Alternative Hypothesis (H₁):** The mean of monthly cell phone bills today is less than $48.28. These hypotheses are represented visually as: - H₀: [ = ] $48.28 - H₁: [ < ] $48.28 **(b) Explain what it would mean to make a Type I error.** A Type I error occurs when the null hypothesis is true, but we mistakenly reject it. In this context, it means concluding that the mean monthly cell phone bill has decreased from $48.28 when, in reality, it has not. **(c) Explain what it would mean to make a Type II error.** A Type II error happens when the null hypothesis is false, but we fail to reject it. Here, it implies failing to recognize that the mean monthly cell phone bill is actually less than $48.28 when it has indeed decreased.
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