A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![You are conducting a study to determine if the proportion of voters who prefer the Democratic candidate is significantly smaller than 74% at a significance level of α = 0.01. According to your sample, 55 out of 79 potential voters prefer the Democratic candidate.
### Steps and Details:
**a. For this study, we should use**
- **Select an answer** [Drop-down options not visible]
**b. The null and alternative hypotheses would be:**
- **Ho:** ? = **Select an answer** (please enter a decimal)
- **H1:** ? = **Select an answer** (Please enter a decimal)
**c. The test statistic ? =**
- **[Entry box]** (please show your answer to 3 decimal places.)
**d. The p-value =**
- **[Entry box]** (Please show your answer to 4 decimal places.)
**e. The p-value is ? α**
- **Select an answer** [Drop-down options not visible]
**f. Based on this, we should**
- **Select an answer** the null hypothesis.
**g. Thus, the final conclusion is that …**
- The data suggest the population proportion is significantly smaller than 74% at α = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 74%.
- The data suggest the population proportion is not significantly smaller than 74% at α = 0.01, so there is no sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 74%.
- The data suggest the population proportion is not significantly smaller than 74% at α = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 74%.
**h. Interpret the p-value in the context of the study.**
- If the population proportion of voters who prefer the Democratic candidate is 74% and if another 79 voters are surveyed then there would be an 18.74% chance fewer than 70% of the 79 voters surveyed prefer the Democratic candidate.
- There is a 74% chance of a Type I error.
- If the sample proportion of voters who prefer the Democratic candidate is 70% and if another 79 voters are surveyed then there would be a 18.74% chance of concluding that fewer than 74%](https://content.bartleby.com/qna-images/question/86a97586-a754-4991-ba2c-c699a7133d3e/1d9850f2-c3ba-4330-aced-62cd7c3a22dc/8nc0nk_processed.jpeg)
Transcribed Image Text:You are conducting a study to determine if the proportion of voters who prefer the Democratic candidate is significantly smaller than 74% at a significance level of α = 0.01. According to your sample, 55 out of 79 potential voters prefer the Democratic candidate.
### Steps and Details:
**a. For this study, we should use**
- **Select an answer** [Drop-down options not visible]
**b. The null and alternative hypotheses would be:**
- **Ho:** ? = **Select an answer** (please enter a decimal)
- **H1:** ? = **Select an answer** (Please enter a decimal)
**c. The test statistic ? =**
- **[Entry box]** (please show your answer to 3 decimal places.)
**d. The p-value =**
- **[Entry box]** (Please show your answer to 4 decimal places.)
**e. The p-value is ? α**
- **Select an answer** [Drop-down options not visible]
**f. Based on this, we should**
- **Select an answer** the null hypothesis.
**g. Thus, the final conclusion is that …**
- The data suggest the population proportion is significantly smaller than 74% at α = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 74%.
- The data suggest the population proportion is not significantly smaller than 74% at α = 0.01, so there is no sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 74%.
- The data suggest the population proportion is not significantly smaller than 74% at α = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 74%.
**h. Interpret the p-value in the context of the study.**
- If the population proportion of voters who prefer the Democratic candidate is 74% and if another 79 voters are surveyed then there would be an 18.74% chance fewer than 70% of the 79 voters surveyed prefer the Democratic candidate.
- There is a 74% chance of a Type I error.
- If the sample proportion of voters who prefer the Democratic candidate is 70% and if another 79 voters are surveyed then there would be a 18.74% chance of concluding that fewer than 74%
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