From previous studies, it is concluded that 39% of phone numbers in a certain city are unlisted. A researcher claims it has decreased and decides to survey 100 adults. Test the researcher's claim at the a = 0.05 significance level. Preliminary: a. Is it safe to assume that n < 0.05 of all subjects in the population? O No O Yes b. Verify np (1 -p) > 10. Round your answer to one decimal place.

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**From previous studies, it is concluded that 39% of phone numbers in a certain city are unlisted. A researcher claims it has decreased and decides to survey 100 adults. Test the researcher’s claim at the α = 0.05 significance level.**

**Preliminary:**

a. Is it safe to assume that n ≤ 0.05 of all subjects in the population?

- ○ No
- ○ Yes

b. Verify \( n\hat{p}(1 - \hat{p}) \geq 10 \). Round your answer to one decimal place.

\[ n\hat{p}(1 - \hat{p}) = \underline{\hspace{3cm}} \]

**Test the claim:**

a. Express the null and alternative hypotheses in symbolic form for this claim.

- \( H_0: \underline{\hspace{5cm}} \)
- \( H_a: \underline{\hspace{5cm}} \) 

*Use the following codes to enter the following symbols:*

- \(\ge\) enter >=
- \(\le\) enter <=
- \(\neq\) enter !=

b. After surveying 100 adult Americans, the researcher finds that 45 phone numbers in a certain city are unlisted. Compute the test statistic. *Round to two decimal places.*

\[ z = \underline{\hspace{3cm}} \]

c. What is the \( p \)-value? *Round to 4 decimals.*

\[ p = \underline{\hspace{3cm}} \]

d. Make a decision based on α = 0.05 significance level.

- ○ Reject the null hypothesis.
- ○ Do not reject the null hypothesis.

e. What is the conclusion?

- ○ There is not sufficient evidence to support the claim that 39% of phone numbers in a certain city are unlisted has decreased.
- ○ There is sufficient evidence to support the claim that 39% of phone numbers in a certain city are unlisted has decreased.

**Note:** The provided text appears to guide through hypothesis testing, including calculating test statistics and p-values while making decisions based on the results.
Transcribed Image Text:**From previous studies, it is concluded that 39% of phone numbers in a certain city are unlisted. A researcher claims it has decreased and decides to survey 100 adults. Test the researcher’s claim at the α = 0.05 significance level.** **Preliminary:** a. Is it safe to assume that n ≤ 0.05 of all subjects in the population? - ○ No - ○ Yes b. Verify \( n\hat{p}(1 - \hat{p}) \geq 10 \). Round your answer to one decimal place. \[ n\hat{p}(1 - \hat{p}) = \underline{\hspace{3cm}} \] **Test the claim:** a. Express the null and alternative hypotheses in symbolic form for this claim. - \( H_0: \underline{\hspace{5cm}} \) - \( H_a: \underline{\hspace{5cm}} \) *Use the following codes to enter the following symbols:* - \(\ge\) enter >= - \(\le\) enter <= - \(\neq\) enter != b. After surveying 100 adult Americans, the researcher finds that 45 phone numbers in a certain city are unlisted. Compute the test statistic. *Round to two decimal places.* \[ z = \underline{\hspace{3cm}} \] c. What is the \( p \)-value? *Round to 4 decimals.* \[ p = \underline{\hspace{3cm}} \] d. Make a decision based on α = 0.05 significance level. - ○ Reject the null hypothesis. - ○ Do not reject the null hypothesis. e. What is the conclusion? - ○ There is not sufficient evidence to support the claim that 39% of phone numbers in a certain city are unlisted has decreased. - ○ There is sufficient evidence to support the claim that 39% of phone numbers in a certain city are unlisted has decreased. **Note:** The provided text appears to guide through hypothesis testing, including calculating test statistics and p-values while making decisions based on the results.
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