From previous studies, it is concluded that 90% of phone numbers in a certain city are unlisted. A researcher claims that the proportion is smaller than 90% and decides to survey 800 working adults. the researcher's claim at the a = 0.01 significance level. Preliminary: a. Is it safe to assume that n< 0.05 of all subjects in the population? Yes No

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From previous studies, it is concluded that 90% of phone numbers in a certain city are unlisted. A researcher claims that the proportion is smaller than 90% and decides to survey 800 working adults. Test the researcher’s claim at the \( \alpha = 0.01 \) significance level.

**Preliminary:**

a. Is it safe to assume that \( n \leq 0.05 \) of all subjects in the population?

- [ ] Yes
- [ ] No

b. Verify \( np(1 - p) \geq 10 \). Round your answer to one decimal place.

\[ np(1 - p) = \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad} \]

**Test the claim:**

a. The null and alternative hypotheses are:

- [ ] \( H_0: \mu = 0.9 \)  
   \( H_a: \mu \neq 0.9 \)
   
- [ ] \( H_0: \mu \geq 0.9 \)  
  \( H_a: \mu < 0.9 \)

- [ ] \( H_0: \mu \leq 0.9 \)  
  \( H_a: \mu > 0.9 \)

- [ ] \( H_0: p = 0.9 \)  
  \( H_a: p \neq 0.9 \)

- [ ] \( H_0: p \geq 0.9 \)  
  \( H_a: p < 0.9 \)

- [ ] \( H_0: p \leq 0.9 \)  
  \( H_a: p > 0.9 \)

b. The test is:

- [ Select an answer ]

c. Based on the sample of 800 people, 81% phone numbers in a certain city are unlisted. What is the test statistic? Round your answer to two decimal places.

\[ \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad} \]

d. What is the p-value? Round your answer to four decimal places.

\[ \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad} \]

e. Make a decision.

- [
Transcribed Image Text:From previous studies, it is concluded that 90% of phone numbers in a certain city are unlisted. A researcher claims that the proportion is smaller than 90% and decides to survey 800 working adults. Test the researcher’s claim at the \( \alpha = 0.01 \) significance level. **Preliminary:** a. Is it safe to assume that \( n \leq 0.05 \) of all subjects in the population? - [ ] Yes - [ ] No b. Verify \( np(1 - p) \geq 10 \). Round your answer to one decimal place. \[ np(1 - p) = \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad} \] **Test the claim:** a. The null and alternative hypotheses are: - [ ] \( H_0: \mu = 0.9 \) \( H_a: \mu \neq 0.9 \) - [ ] \( H_0: \mu \geq 0.9 \) \( H_a: \mu < 0.9 \) - [ ] \( H_0: \mu \leq 0.9 \) \( H_a: \mu > 0.9 \) - [ ] \( H_0: p = 0.9 \) \( H_a: p \neq 0.9 \) - [ ] \( H_0: p \geq 0.9 \) \( H_a: p < 0.9 \) - [ ] \( H_0: p \leq 0.9 \) \( H_a: p > 0.9 \) b. The test is: - [ Select an answer ] c. Based on the sample of 800 people, 81% phone numbers in a certain city are unlisted. What is the test statistic? Round your answer to two decimal places. \[ \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad} \] d. What is the p-value? Round your answer to four decimal places. \[ \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad} \] e. Make a decision. - [
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