Answer A B C ### Hypothesis Testing for Proportion of King County Residents Living in Seattle4. **2010 Census Analysis for King County Residents** The 2010 Census data indicated that 31% of King County residents lived within Seattle city limits. Seattle city officials are investigating if the current proportion of county residents living in Seattle exceeds the 2010 level. a. **Define Your Parameter and Hypotheses** - **Parameter Definition**: The parameter of interest is the true proportion of King County residents currently living within Seattle city limits. - **Null Hypothesis ($H_0$)**: $ p = 0.31 $, which states that the proportion of King County residents living in Seattle has not changed from the 2010 level. - **Alternative Hypothesis ($H_a$)**: $ p > 0.31 $, which indicates that the proportion of King County residents living in Seattle has increased since 2010. b. **Conditions for Hypothesis Testing** To conduct a valid hypothesis test, the following conditions must be met: - **Randomization Condition**: The sample of residents should be randomly selected. Since the problem statement mentions a random selection of 1000 King County residents, this condition is satisfied. - **10% Condition**: The sample size should be less than 10% of the population. Given that 1000 is likely less than 10% of the total King County population, this condition is also satisfied. - **Success/Failure Condition**: We check if $ np \geq 10 $ and $ n(1-p) \geq 10 $. For $ p = 0.31 $, \[ np = 1000 \times 0.31 = 310 \geq 10 \] \[ n(1-p) = 1000 \times 0.69 = 690 \geq 10 \] Hence, the Success/Failure condition is satisfied. c. **Perform Hypothesis Test and Compute the P-Value** Suppose a recent survey shows that out of a sample of 1000 King County residents, 345 live in Seattle city limits. - **Sample Proportion ($ \hat{p} $)**: \[ \hat{p} = \frac{345

a.Here the parameter is defined as: Parameter =population proportion(p)=0.31 The hypothesis to be…

4. The 2010 Census showed that 31% of King Country residents lived within Seattle city limits. Seattle city officials wondered if the proportion of county residents currently living in Seattle is higher than the 2010 level. a. Define your parameter, and write the null hypothesis, alternative hypothesis for hypothesis testing. b. Show that the necessary conditions (Randomization Condition, 10% Condition, Success/Failure Condition) are satisfied if they randomly select a sample of 1000 King County residents. Briefly explain how each condition is satisfied. c. Suppose that out of a recent sample of 1000 King County residents, 345 lived in Seattle city limits. Perform the hypothesis test and compute the P-value.

4. The 2010 Census showed that 31% of King Country residents lived within Seattle city limits. Seattle city officials wondered if the proportion of county residents currently living in Seattle is higher than the 2010 level. a. Define your parameter, and write the null hypothesis, alternative hypothesis for hypothesis testing. b. Show that the necessary conditions (Randomization Condition, 10% Condition, Success/Failure Condition) are satisfied if they randomly select a sample of 1000 King County residents. Briefly explain how each condition is satisfied. c. Suppose that out of a recent sample of 1000 King County residents, 345 lived in Seattle city limits. Perform the hypothesis test and compute the P-value.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Answer A B C

### Hypothesis Testing for Proportion of King County Residents Living in Seattle

4. **2010 Census Analysis for King County Residents**

The 2010 Census data indicated that 31% of King County residents lived within Seattle city limits. Seattle city officials are investigating if the current proportion of county residents living in Seattle exceeds the 2010 level.

a. **Define Your Parameter and Hypotheses**

- **Parameter Definition**: The parameter of interest is the true proportion of King County residents currently living within Seattle city limits.
- **Null Hypothesis ($H_0$)**: $ p = 0.31 $, which states that the proportion of King County residents living in Seattle has not changed from the 2010 level.
- **Alternative Hypothesis ($H_a$)**: $ p > 0.31 $, which indicates that the proportion of King County residents living in Seattle has increased since 2010.

b. **Conditions for Hypothesis Testing**

To conduct a valid hypothesis test, the following conditions must be met:

- **Randomization Condition**: The sample of residents should be randomly selected.
Since the problem statement mentions a random selection of 1000 King County residents, this condition is satisfied.
- **10% Condition**: The sample size should be less than 10% of the population.
Given that 1000 is likely less than 10% of the total King County population, this condition is also satisfied.
- **Success/Failure Condition**: We check if $ np \geq 10 $ and $ n(1-p) \geq 10 $.
For $ p = 0.31 $,
\[
np = 1000 \times 0.31 = 310 \geq 10
\]
\[
n(1-p) = 1000 \times 0.69 = 690 \geq 10
\]
Hence, the Success/Failure condition is satisfied.

c. **Perform Hypothesis Test and Compute the P-Value**

Suppose a recent survey shows that out of a sample of 1000 King County residents, 345 live in Seattle city limits.

- **Sample Proportion ($ \hat{p} $)**:
\[
\hat{p} = \frac{345

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