Forty students at a local high school are polled on if they have smoked before. The results are that 23 have not and 17 have smoked. O JMP Applet mp Distributions Smoked? Frequencies Test Probabilities Level Estim Prob Hypoth Prob 0.75000 0.25000 z Test Prob > |z| Test Statistic 2.5560 0.0106* Level Count Prob N 23 0.57500 N 0.57500 Y 17 0.42500 Y 0.42500 Total 40 1.00000 N Missing 2 Levels Method: Fix hypothesized values, rescale omitted Click here to access the JMP applet in a new window. O (a) The national average of high school students who have smoked is 25% and a company is interested in seeing if this particular high schoo a statistically different proportion of smokers. What is the hypothesis test? O H;: < 0.25 Hiµ > 0.25 Ο Η: με 0.25 H,: u = 0.25 O Ho: p = 0.25 H:p = 0.25 O Ho:p = 0.25 H:p > 0.25 O Ho:p > 0.25 H:p < 0.25 O (b) Give the test statistic for the given hypothesis test. (Enter your answer to four decimal places.)

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**JMP Applet Analysis**

**Overview:**
Forty students at a local high school are surveyed to determine if they have smoked before. The results show that 23 students have not smoked, while 17 have smoked.

**JMP Applet:**
- **Graph Description:** 
  - The bar chart displays two categories: "N" (No) and "Y" (Yes).
  - "N" corresponds to 23 students and "Y" corresponds to 17 students.

- **Frequencies Table:**
  - Level: N (No) | Count: 23 | Proportion (Prob): 0.57500
  - Level: Y (Yes) | Count: 17 | Proportion (Prob): 0.42500
  - Total: 40 students | Proportion Total: 1.00000

- **Test Probabilities Table:**
  - Level | Estim Prob | Hypoth Prob
  - N | 0.57500 | 0.75000
  - Y | 0.42500 | 0.25000
  - Test Statistic: 2.5560
  - Probability (Prob > |z|): 0.0106*
  - Method: Fix hypothesized values, rescale omitted

**Click here to access the JMP applet in a new window.**

---

**Hypothesis Testing**

**(a) Determining Hypothesis:**

The national average of high school students who have smoked is 25%, and a company is interested in examining if this particular high school has a statistically different proportion of smokers. What is the hypothesis test?

- \( H_0: p = 0.25 \)
- \( H_1: p \neq 0.25 \)

**(b) Test Statistic Calculation:**

Provide the test statistic for the given hypothesis test. (Enter your answer to four decimal places.)

- \( z = \underline{\phantom{xxxx}} \)
Transcribed Image Text:**JMP Applet Analysis** **Overview:** Forty students at a local high school are surveyed to determine if they have smoked before. The results show that 23 students have not smoked, while 17 have smoked. **JMP Applet:** - **Graph Description:** - The bar chart displays two categories: "N" (No) and "Y" (Yes). - "N" corresponds to 23 students and "Y" corresponds to 17 students. - **Frequencies Table:** - Level: N (No) | Count: 23 | Proportion (Prob): 0.57500 - Level: Y (Yes) | Count: 17 | Proportion (Prob): 0.42500 - Total: 40 students | Proportion Total: 1.00000 - **Test Probabilities Table:** - Level | Estim Prob | Hypoth Prob - N | 0.57500 | 0.75000 - Y | 0.42500 | 0.25000 - Test Statistic: 2.5560 - Probability (Prob > |z|): 0.0106* - Method: Fix hypothesized values, rescale omitted **Click here to access the JMP applet in a new window.** --- **Hypothesis Testing** **(a) Determining Hypothesis:** The national average of high school students who have smoked is 25%, and a company is interested in examining if this particular high school has a statistically different proportion of smokers. What is the hypothesis test? - \( H_0: p = 0.25 \) - \( H_1: p \neq 0.25 \) **(b) Test Statistic Calculation:** Provide the test statistic for the given hypothesis test. (Enter your answer to four decimal places.) - \( z = \underline{\phantom{xxxx}} \)
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