It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 200 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a lower percentage of left-handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type Il errors in the context of this problem. a) The symbol for the random variable involved in this problem is ? v The wording for the random variable in context is as follows: Select an answer b) The symbol for the parameter involved in this problem is ? The wording for the parameter in context is as follows: Select an answer c) Fill in the correct null and alternative hypotheses: Ho: ? HA:

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**Understanding Hypothesis Testing in the Context of Left-Handedness**

It is believed that 11% of all Americans are left-handed. A college needs to determine how many left-handed desks to place in the large lecture halls being constructed on its campus. In a random sample of 200 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a lower percentage of left-handers than the general American population. This involves stating the random variable, population parameter, and hypotheses, and understanding Type I and Type II errors in this context.

### a) Random Variable

- **Symbol for the random variable:** \( \hat{p} \)
- **Contextual wording for the random variable:** The proportion of left-handed students in the sample of 200 students.

### b) Population Parameter

- **Symbol for the parameter:** \( p \)
- **Contextual wording for the parameter:** The proportion of all students at the college who are left-handed.

### c) Null and Alternative Hypotheses

- **Null Hypothesis (\( H_0 \)):** \( p = 0.11 \)
  - The proportion of left-handed students at the college is equal to 11%, the national average.
- **Alternative Hypothesis (\( H_A \)):** \( p < 0.11 \)
  - The proportion of left-handed students at the college is less than 11%.

### d) Type I Error

- **Definition Context:** A Type I error would occur if the college concludes that the proportion of left-handed students is lower than 11% when, in fact, it is not.

### e) Type II Error

- **Definition Context:** A Type II error would occur if the college fails to conclude that the proportion of left-handed students is lower than 11% when, in fact, it is lower.

Understanding these statistical terms helps in making informed decisions based on the hypothesis testing results.
Transcribed Image Text:**Understanding Hypothesis Testing in the Context of Left-Handedness** It is believed that 11% of all Americans are left-handed. A college needs to determine how many left-handed desks to place in the large lecture halls being constructed on its campus. In a random sample of 200 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a lower percentage of left-handers than the general American population. This involves stating the random variable, population parameter, and hypotheses, and understanding Type I and Type II errors in this context. ### a) Random Variable - **Symbol for the random variable:** \( \hat{p} \) - **Contextual wording for the random variable:** The proportion of left-handed students in the sample of 200 students. ### b) Population Parameter - **Symbol for the parameter:** \( p \) - **Contextual wording for the parameter:** The proportion of all students at the college who are left-handed. ### c) Null and Alternative Hypotheses - **Null Hypothesis (\( H_0 \)):** \( p = 0.11 \) - The proportion of left-handed students at the college is equal to 11%, the national average. - **Alternative Hypothesis (\( H_A \)):** \( p < 0.11 \) - The proportion of left-handed students at the college is less than 11%. ### d) Type I Error - **Definition Context:** A Type I error would occur if the college concludes that the proportion of left-handed students is lower than 11% when, in fact, it is not. ### e) Type II Error - **Definition Context:** A Type II error would occur if the college fails to conclude that the proportion of left-handed students is lower than 11% when, in fact, it is lower. Understanding these statistical terms helps in making informed decisions based on the hypothesis testing results.
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