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You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 65% at a level of significance of a = 0.05. According to your sample, 66 out of 94 potential voters prefer the Democratic candidate. a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? v|| Select an answer v (please enter a decimal) H1:? v||Select an answer (Please enter a decimal) c. The test statistic ? v = (please show your answer to 3 decimal places.)

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 65% at a level of significance of a = 0.05. According to your sample, 66 out of 94 potential voters prefer the Democratic candidate. a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? v|| Select an answer v (please enter a decimal) H1:? v||Select an answer (Please enter a decimal) c. The test statistic ? v = (please show your answer to 3 decimal places.)

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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The text appears to be part of an educational assignment related to statistical analysis. The focus is on interpreting p-values and levels of significance in the context of a study concerning voter preferences. --- **g.** The data suggest the population proportion is **significantly** larger than 65% at α = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 65%. **h. Interpret the p-value in the context of the study.** - **Option 1:** If the population proportion of voters who prefer the Democratic candidate is 65% and if another 94 voters are surveyed, then there would be a 14.47% chance that more than 70% of the 94 voters surveyed prefer the Democratic candidate. - **Option 2:** There is a 14.47% chance that more than 65% of all voters prefer the Democratic candidate. - **Option 3:** If the sample proportion of voters who prefer the Democratic candidate is 70% and if another 94 voters are surveyed, then there would be a 14.47% chance of concluding that more than 65% of all voters surveyed prefer the Democratic candidate. - **Option 4:** There is a 14.47% chance of a Type I error. **i. Interpret the level of significance in the context of the study.** - **Option 1:** If the proportion of voters who prefer the Democratic candidate is larger than 65% and if another 94 voters are surveyed, then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 65%. - **Option 2:** There is a 5% chance that the proportion of voters who prefer the Democratic candidate is larger than 65%. - **Option 3:** There is a 5% chance that the earth is flat and we never actually sent a man to the moon. - **Option 4:** If the population proportion of voters who prefer the Democratic candidate is 65% and if another 94 voters are surveyed, then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is larger than 65%. --- **Submit Question** This text explores the interpretation of statistical results and decisions, emphasizing understanding p-values, Type I errors
Transcribed Image Text:The text appears to be part of an educational assignment related to statistical analysis. The focus is on interpreting p-values and levels of significance in the context of a study concerning voter preferences. --- **g.** The data suggest the population proportion is **significantly** larger than 65% at α = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 65%. **h. Interpret the p-value in the context of the study.** - **Option 1:** If the population proportion of voters who prefer the Democratic candidate is 65% and if another 94 voters are surveyed, then there would be a 14.47% chance that more than 70% of the 94 voters surveyed prefer the Democratic candidate. - **Option 2:** There is a 14.47% chance that more than 65% of all voters prefer the Democratic candidate. - **Option 3:** If the sample proportion of voters who prefer the Democratic candidate is 70% and if another 94 voters are surveyed, then there would be a 14.47% chance of concluding that more than 65% of all voters surveyed prefer the Democratic candidate. - **Option 4:** There is a 14.47% chance of a Type I error. **i. Interpret the level of significance in the context of the study.** - **Option 1:** If the proportion of voters who prefer the Democratic candidate is larger than 65% and if another 94 voters are surveyed, then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 65%. - **Option 2:** There is a 5% chance that the proportion of voters who prefer the Democratic candidate is larger than 65%. - **Option 3:** There is a 5% chance that the earth is flat and we never actually sent a man to the moon. - **Option 4:** If the population proportion of voters who prefer the Democratic candidate is 65% and if another 94 voters are surveyed, then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is larger than 65%. --- **Submit Question** This text explores the interpretation of statistical results and decisions, emphasizing understanding p-values, Type I errors
**Title: Analyzing Voter Preferences: Hypothesis Testing** **Objective:** Conduct a study to determine if the proportion of voters preferring the Democratic candidate is significantly greater than 65% at a significance level of \( \alpha = 0.05 \). The sample data consists of 66 out of 94 potential voters favoring the Democratic candidate. **Steps for Hypothesis Testing:** a. **Test Selection:** - Choose the appropriate statistical test (select from options like Z-test, t-test, etc.). b. **Formulate Hypotheses:** - **Null Hypothesis (\( H_0 \)):** The proportion of voters preferring the Democratic candidate is 0.65. - **Alternative Hypothesis (\( H_1 \)):** The proportion of voters preferring the Democratic candidate is greater than 0.65. c. **Calculate the Test Statistic (\( z \)):** - Use the formula for the test statistic and report to three decimal places. d. **Determine the p-value:** - Compute the p-value and express it to four decimal places. e. **Compare the p-value and Significance Level (\( \alpha \)):** - Determine if the p-value is less than or greater than \( \alpha \). f. **Decision Rule:** - Based on the comparison, decide whether to reject or fail to reject the null hypothesis. g. **Conclusion:** - Depending on the decision in step f, select the appropriate conclusion: - The data suggest the population proportion is not significantly larger than 65%. - There is insufficient evidence to conclude a larger proportion at \( \alpha = 0.05 \). - Alternatively, the data suggest a significant increase at the same significance level. h. **Interpretation of the p-value:** - If the population proportion is 65%, and assuming random sampling of 94 voters, interpret the likelihood of observing a sample proportion of 70%. - Consider the implications of the calculated p-value (e.g., chance of observing results as extreme or more extreme than the sample). **Summary:** The hypothesis test will tell us if the preference for the Democratic candidate among the sampled voters is convincingly over 65% or if it could reasonably be due to random chance. Understanding the role of the p-value and how it relates to the null hypothesis is essential for making informed conclusions.
Transcribed Image Text:**Title: Analyzing Voter Preferences: Hypothesis Testing** **Objective:** Conduct a study to determine if the proportion of voters preferring the Democratic candidate is significantly greater than 65% at a significance level of \( \alpha = 0.05 \). The sample data consists of 66 out of 94 potential voters favoring the Democratic candidate. **Steps for Hypothesis Testing:** a. **Test Selection:** - Choose the appropriate statistical test (select from options like Z-test, t-test, etc.). b. **Formulate Hypotheses:** - **Null Hypothesis (\( H_0 \)):** The proportion of voters preferring the Democratic candidate is 0.65. - **Alternative Hypothesis (\( H_1 \)):** The proportion of voters preferring the Democratic candidate is greater than 0.65. c. **Calculate the Test Statistic (\( z \)):** - Use the formula for the test statistic and report to three decimal places. d. **Determine the p-value:** - Compute the p-value and express it to four decimal places. e. **Compare the p-value and Significance Level (\( \alpha \)):** - Determine if the p-value is less than or greater than \( \alpha \). f. **Decision Rule:** - Based on the comparison, decide whether to reject or fail to reject the null hypothesis. g. **Conclusion:** - Depending on the decision in step f, select the appropriate conclusion: - The data suggest the population proportion is not significantly larger than 65%. - There is insufficient evidence to conclude a larger proportion at \( \alpha = 0.05 \). - Alternatively, the data suggest a significant increase at the same significance level. h. **Interpretation of the p-value:** - If the population proportion is 65%, and assuming random sampling of 94 voters, interpret the likelihood of observing a sample proportion of 70%. - Consider the implications of the calculated p-value (e.g., chance of observing results as extreme or more extreme than the sample). **Summary:** The hypothesis test will tell us if the preference for the Democratic candidate among the sampled voters is convincingly over 65% or if it could reasonably be due to random chance. Understanding the role of the p-value and how it relates to the null hypothesis is essential for making informed conclusions.
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Sample size (n)  =94

Number of voters preferring Democratic (x) = 66

 

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