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f. Based on this, we should reject g. Thus, the final conclusion is that ... X the null hypothesis. X O The data suggest the populaton proportion is significantly different from 62% at a = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 62% The data suggest the population proportion is not significantly different from 62% at x = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 62%. O The data suggest the population proportion is not significantly different from 62% at a = 0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 62%. X h. Interpret the p-value in the context of the study. O There is a 24.38% chance that the percent of all voters who prefer the Democratic candidate differs from 62%. O There is a 24.38% chance of a Type I error. If the sample proportion of voters who prefer the Democratic candidate is 53% and if another 50 voters are surveyed then there would be a 24.38% chance that we would conclude either fewer than 62% of all voters prefer the Democratic candidate or more than 62% of all voters prefer the Democratic candidate. O If the population proportion of voters who prefer the Democratic candidate is 62% and if another 50 voters are surveyed then there would be a 24.38% chance that either fewer than 53% of the 50 voters surveyed prefer the Democratic candidate or more than 71% of the 50 voters surveyed prefer the Democratic candidate.

f. Based on this, we should reject g. Thus, the final conclusion is that ... X the null hypothesis. X O The data suggest the populaton proportion is significantly different from 62% at a = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 62% The data suggest the population proportion is not significantly different from 62% at x = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 62%. O The data suggest the population proportion is not significantly different from 62% at a = 0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 62%. X h. Interpret the p-value in the context of the study. O There is a 24.38% chance that the percent of all voters who prefer the Democratic candidate differs from 62%. O There is a 24.38% chance of a Type I error. If the sample proportion of voters who prefer the Democratic candidate is 53% and if another 50 voters are surveyed then there would be a 24.38% chance that we would conclude either fewer than 62% of all voters prefer the Democratic candidate or more than 62% of all voters prefer the Democratic candidate. O If the population proportion of voters who prefer the Democratic candidate is 62% and if another 50 voters are surveyed then there would be a 24.38% chance that either fewer than 53% of the 50 voters surveyed prefer the Democratic candidate or more than 71% of the 50 voters surveyed prefer the Democratic candidate.

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
Problem 1P
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### Analysis of Voter Preferences **f. Conclusion Based on the Hypothesis Test:** - We should **reject** the null hypothesis. **g. Final Conclusion:** - The correct option highlighted is: - "The data suggest the population proportion is not significantly different from 62% at α = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 62%." **h. Interpretation of the p-value in Context:** - The correct interpretation highlighted is: - "If the sample proportion of voters who prefer the Democratic candidate is 53% and if another 50 voters are surveyed, then there would be a 24.38% chance that we would conclude either fewer than 62% of all voters prefer the Democratic candidate or more than 62% of all voters prefer the Democratic candidate." **i. Interpretation of the Level of Significance:** - The correct interpretation highlighted is: - "If the population proportion of voters who prefer the Democratic candidate is 62% and if another 50 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 different from 62%." These selections provide insights into how statistical evidence from the data was analyzed. The p-value and level of significance (α = 0.05) are crucial in determining the strength and validity of the conclusions drawn from the voter survey data.
Transcribed Image Text:### Analysis of Voter Preferences **f. Conclusion Based on the Hypothesis Test:** - We should **reject** the null hypothesis. **g. Final Conclusion:** - The correct option highlighted is: - "The data suggest the population proportion is not significantly different from 62% at α = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 62%." **h. Interpretation of the p-value in Context:** - The correct interpretation highlighted is: - "If the sample proportion of voters who prefer the Democratic candidate is 53% and if another 50 voters are surveyed, then there would be a 24.38% chance that we would conclude either fewer than 62% of all voters prefer the Democratic candidate or more than 62% of all voters prefer the Democratic candidate." **i. Interpretation of the Level of Significance:** - The correct interpretation highlighted is: - "If the population proportion of voters who prefer the Democratic candidate is 62% and if another 50 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 different from 62%." These selections provide insights into how statistical evidence from the data was analyzed. The p-value and level of significance (α = 0.05) are crucial in determining the strength and validity of the conclusions drawn from the voter survey data.
You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 62% at a level of significance of α = 0.05. According to your sample, 27 out of 50 potential voters prefer the Democratic candidate. a. For this study, we should use a **z-test for a population proportion**. b. The null and alternative hypotheses would be: - Null Hypothesis (H₀): p = 0.62 - Alternative Hypothesis (H₁): p ≠ 0.62 c. The test statistic \( z \) is -1.165 (please show your answer to 3 decimal places). d. The p-value = 0.1248 (please show your answer to 4 decimal places). e. The p-value is \( > \) α. f. Based on this, we should **not reject** the null hypothesis. g. Thus, the final conclusion is that: - The data suggest the population proportion is **not significantly different** from 62% at α = 0.05, so there is insufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 62%.
Transcribed Image Text:You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 62% at a level of significance of α = 0.05. According to your sample, 27 out of 50 potential voters prefer the Democratic candidate. a. For this study, we should use a **z-test for a population proportion**. b. The null and alternative hypotheses would be: - Null Hypothesis (H₀): p = 0.62 - Alternative Hypothesis (H₁): p ≠ 0.62 c. The test statistic \( z \) is -1.165 (please show your answer to 3 decimal places). d. The p-value = 0.1248 (please show your answer to 4 decimal places). e. The p-value is \( > \) α. f. Based on this, we should **not reject** the null hypothesis. g. Thus, the final conclusion is that: - The data suggest the population proportion is **not significantly different** from 62% at α = 0.05, so there is insufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 62%.
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