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In a previous year, 62% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 700 females aged 15 and older and finds that 428 are living alone. Is there sufficient evidence at the a=0.1 level of significance to conclude the proportion has changed? Because npo (1-Po) =10, the sample size is (Round to one decimal place as needed.) C 5% of the population size, and the sample a random sample, all of the requirements for testing the hypothesis satisfied.

In a previous year, 62% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 700 females aged 15 and older and finds that 428 are living alone. Is there sufficient evidence at the a=0.1 level of significance to conclude the proportion has changed? Because npo (1-Po) =10, the sample size is (Round to one decimal place as needed.) C 5% of the population size, and the sample a random sample, all of the requirements for testing the hypothesis satisfied.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**Hypothesis Testing for Proportion** **Context:** In a previous year, 62% of females aged 15 and older lived alone. A sociologist is examining whether this percentage has changed by conducting a random sample of 700 females in this age group. The study finds that 428 are living alone. The question is whether there is sufficient evidence at the $\alpha = 0.1$ level of significance to conclude that the proportion has changed. --- **Hypothesis Test Requirements:** - **Sample Size Requirement:** \[ np_0(1 - p_0) = \_\_\_ \geq 10 \] (Fill in the blank with the calculated value to ensure the sample size condition is met.) - **Population Proportion's 5% Rule:** - The sample size is \_\_\_\_ 5% of the population size. (State whether more than, less than, or equal to.) - **Random Sample Condition:** - The sample \_\_\_\_ a random sample. (Indicate if this condition is met.) - **Overall Requirements Check:** - All the requirements for testing the hypothesis \_\_\_\_ satisfied. (State whether satisfied or not.) **Instructions:** Complete the blanks with appropriate values and terms. Round any necessary values to one decimal place as instructed. **Note:** This exercise guides you through evaluating the conditions necessary for hypothesis testing concerning population proportions.
Transcribed Image Text:**Hypothesis Testing for Proportion** **Context:** In a previous year, 62% of females aged 15 and older lived alone. A sociologist is examining whether this percentage has changed by conducting a random sample of 700 females in this age group. The study finds that 428 are living alone. The question is whether there is sufficient evidence at the $\alpha = 0.1$ level of significance to conclude that the proportion has changed. --- **Hypothesis Test Requirements:** - **Sample Size Requirement:** \[ np_0(1 - p_0) = \_\_\_ \geq 10 \] (Fill in the blank with the calculated value to ensure the sample size condition is met.) - **Population Proportion's 5% Rule:** - The sample size is \_\_\_\_ 5% of the population size. (State whether more than, less than, or equal to.) - **Random Sample Condition:** - The sample \_\_\_\_ a random sample. (Indicate if this condition is met.) - **Overall Requirements Check:** - All the requirements for testing the hypothesis \_\_\_\_ satisfied. (State whether satisfied or not.) **Instructions:** Complete the blanks with appropriate values and terms. Round any necessary values to one decimal place as instructed. **Note:** This exercise guides you through evaluating the conditions necessary for hypothesis testing concerning population proportions.
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### Hypothesis Testing on Proportion Change In a previous year, 62% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 700 females aged 15 and older and finds that 428 are living alone. Is there sufficient evidence at the α = 0.1 level of significance to conclude the proportion has changed? --- #### Requirements for Hypothesis Testing - Given: \( n p_0 (1 - p_0) = 164.9 \) - Since \( 164.9 > 10 \), the sample size is less than 5% of the population size, and the sample is a random sample, all of the requirements for testing the hypothesis are satisfied. #### Hypotheses - **Null Hypothesis (\( H_0 \))**: \( p = 0.62 \) - **Alternative Hypothesis (\( H_1 \))**: \( p \neq 0.62 \) #### Test Statistic Calculation - Computed test statistic, \( z_0 = -0.47 \) - (Value rounded to two decimal places as needed.) #### P-Value Determination - Calculated P-value = 0.639 - (Value rounded to three decimal places as needed.) #### Conclusion - Since the P-value is greater than \( \alpha \) (0.1), \( H_0 \) is not rejected. - There is not sufficient evidence at the \( \alpha = 0.1 \) level of significance to conclude that the proportion of females aged 15 and older who are living alone has changed. This example demonstrates the steps in performing hypothesis testing for a proportion. The key aspects include calculating test statistics, determining the P-value, and drawing conclusions based on the level of significance.
Transcribed Image Text:### Hypothesis Testing on Proportion Change In a previous year, 62% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 700 females aged 15 and older and finds that 428 are living alone. Is there sufficient evidence at the α = 0.1 level of significance to conclude the proportion has changed? --- #### Requirements for Hypothesis Testing - Given: \( n p_0 (1 - p_0) = 164.9 \) - Since \( 164.9 > 10 \), the sample size is less than 5% of the population size, and the sample is a random sample, all of the requirements for testing the hypothesis are satisfied. #### Hypotheses - **Null Hypothesis (\( H_0 \))**: \( p = 0.62 \) - **Alternative Hypothesis (\( H_1 \))**: \( p \neq 0.62 \) #### Test Statistic Calculation - Computed test statistic, \( z_0 = -0.47 \) - (Value rounded to two decimal places as needed.) #### P-Value Determination - Calculated P-value = 0.639 - (Value rounded to three decimal places as needed.) #### Conclusion - Since the P-value is greater than \( \alpha \) (0.1), \( H_0 \) is not rejected. - There is not sufficient evidence at the \( \alpha = 0.1 \) level of significance to conclude that the proportion of females aged 15 and older who are living alone has changed. This example demonstrates the steps in performing hypothesis testing for a proportion. The key aspects include calculating test statistics, determining the P-value, and drawing conclusions based on the level of significance.
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In a previous year, 62% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 700 females aged 15 and older and finds that 428 are living alone. Is there sufficient evidence at the ax = 0.1 level of significance to conclude the proportion has changed? Because npo (1-Po) = 164.9 > 10, the sample size is (Round to one decimal place as needed.) Identify the null and alternative hypotheses for this test. Ho: p = 0.62 versus H₁: р # 0.62 (Type integers or decimals. Do not round.) Find the test statistic for this hypothesis test. Zo (Round to two decimal places as needed.) = less than 5% of the population size, and the sample is a random sample, all of the requirements for testing the hypothesis are satisfied.
Transcribed Image Text:In a previous year, 62% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 700 females aged 15 and older and finds that 428 are living alone. Is there sufficient evidence at the ax = 0.1 level of significance to conclude the proportion has changed? Because npo (1-Po) = 164.9 > 10, the sample size is (Round to one decimal place as needed.) Identify the null and alternative hypotheses for this test. Ho: p = 0.62 versus H₁: р # 0.62 (Type integers or decimals. Do not round.) Find the test statistic for this hypothesis test. Zo (Round to two decimal places as needed.) = less than 5% of the population size, and the sample is a random sample, all of the requirements for testing the hypothesis are satisfied.
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In a previous year, 62% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 700 females aged 15 and older and finds that 428 are living alone. Is there sufficient evidence at the α = 0.1 level of significance to conclude the proportion has changed? --- Because \(np_0 \, (1 - p_0) = 164.9 > 10\), the sample size is less than 5% of the population size, and the sample is a random sample, all of the requirements for testing the hypothesis are satisfied. (Round to one decimal place as needed.) Identify the null and alternative hypotheses for this test. \(H_0:\) \(\_\_\_\_\_\_\) versus \(H_1:\) \(\_\_\_\_\_\_\) (Type integers or decimals. Do not round.)
Transcribed Image Text:In a previous year, 62% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 700 females aged 15 and older and finds that 428 are living alone. Is there sufficient evidence at the α = 0.1 level of significance to conclude the proportion has changed? --- Because \(np_0 \, (1 - p_0) = 164.9 > 10\), the sample size is less than 5% of the population size, and the sample is a random sample, all of the requirements for testing the hypothesis are satisfied. (Round to one decimal place as needed.) Identify the null and alternative hypotheses for this test. \(H_0:\) \(\_\_\_\_\_\_\) versus \(H_1:\) \(\_\_\_\_\_\_\) (Type integers or decimals. Do not round.)
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