(a) A dictator is concerned about his "negatives," that is, the percentage of the country's residents who express disapproval of his job performance. His political committee pays for a series of TV ads, hoping that they can keep the negatives below 44%. They will use follow up polling to assess the ads' effectiveness. Let p be the proportion of the country's residents who express disapproval of the dictator's performance. Ho: P HA: P 0.44 0.44 (b) Is a ten-section spinner fair? Let p represent the probability of the spinner landing on any particular section. Ho: P HA: (c) Only about 19% of people who try to gain self-confidence succeed. Sellers of a motivational tape claim that listening to the recorded messages can help people succeed. Let p be the proportion of people who try to gain self-confidence and succeed. 10

MATLAB: An Introduction with Applications
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The text describes three hypothesis testing scenarios for different situations:

---

**Situation (a):**
A political scenario where a dictator is concerned about the percentage of residents who disapprove of his job performance. The political committee aims to reduce the negatives below 44% through TV advertisements. 

- **Null Hypothesis (H₀):** \( p = 0.44 \)
- **Alternative Hypothesis (Hₐ):** \( p < 0.44 \)

**Situation (b):**
The fairness of a ten-section spinner is in question. The probability of the spinner landing on any particular section is tested.

- **Null Hypothesis (H₀):** \( p = \frac{1}{10} \)
- **Alternative Hypothesis (Hₐ):** \( p \neq \frac{1}{10} \)

**Situation (c):**
It is stated that only about 19% of people attempting to gain self-confidence succeed. There is a claim that motivational tapes help improve this rate.

- **Null Hypothesis (H₀):** \( p = 0.19 \)
- **Alternative Hypothesis (Hₐ):** \( p > 0.19 \)

--- 

In each case, the symbol \( p \) represents the proportion corresponding to the scenario being tested.
Transcribed Image Text:The text describes three hypothesis testing scenarios for different situations: --- **Situation (a):** A political scenario where a dictator is concerned about the percentage of residents who disapprove of his job performance. The political committee aims to reduce the negatives below 44% through TV advertisements. - **Null Hypothesis (H₀):** \( p = 0.44 \) - **Alternative Hypothesis (Hₐ):** \( p < 0.44 \) **Situation (b):** The fairness of a ten-section spinner is in question. The probability of the spinner landing on any particular section is tested. - **Null Hypothesis (H₀):** \( p = \frac{1}{10} \) - **Alternative Hypothesis (Hₐ):** \( p \neq \frac{1}{10} \) **Situation (c):** It is stated that only about 19% of people attempting to gain self-confidence succeed. There is a claim that motivational tapes help improve this rate. - **Null Hypothesis (H₀):** \( p = 0.19 \) - **Alternative Hypothesis (Hₐ):** \( p > 0.19 \) --- In each case, the symbol \( p \) represents the proportion corresponding to the scenario being tested.
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