You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 50% at a level of significance of αα = 0.05. According to your sample, 23 out of 52 potential voters prefer the Democratic candidate.For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be: Ho: ? p μ Select an answer < > = ≠ (please enter a decimal) H1: ? p μ Select an answer = > ≠ < (Please enter a decimal)The test statistic ? t z = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 4 decimal places.)The p-value is ? ≤ > ααBased on this, we should Select an answer fail to reject reject accept the null hypothesis.Thus, the final conclusion is that ...The data suggest the populaton proportion is significantly smaller than 50% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 50%The data suggest the population proportion is not significantly smaller than 50% at αα = 0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 50%.The data suggest the population proportion is not significantly smaller than 50% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 50%.Interpret the p-value in the context of the study.There is a 20.27% chance that fewer than 50% of all voters prefer the Democratic candidate.If the population proportion of voters who prefer the Democratic candidate is 50% and if another 52 voters are surveyed then there would be a 20.27% chance fewer than 45% of the 52 voters surveyed prefer the Democratic candidate.If the sample proportion of voters who prefer the Democratic candidate is 45% and if another 52 voters are surveyed then there would be a 20.27% chance of concluding that fewer than 50% of all voters surveyed prefer the Democratic candidate. There is a 50% chance of a Type I error.Interpret the level of significance in the context of the study.If the proportion of voters who prefer the Democratic candidate is smaller than 50% and if another 52 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 50%.There is a 5% chance that the proportion of voters who prefer the Democratic candidate is smaller than 50%.There is a 5% chance that the earth is flat and we never actually sent a man to the moon.If the population proportion of voters who prefer the Democratic candidate is 50% and if another 52 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 smaller than 50%

Answered: You are conducting a study to see if…

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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You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 50% at a level of significance of αα = 0.05. According to your sample, 23 out of 52 potential voters prefer the Democratic candidate.

For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
The null and alternative hypotheses would be:
Ho: ? p μ Select an answer < > = ≠ (please enter a decimal)
H₁: ? p μ Select an answer = > ≠ < (Please enter a decimal)

The test statistic ? t z = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is ? ≤ > αα
Based on this, we should Select an answer fail to reject reject accept the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the populaton proportion is significantly smaller than 50% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 50%
- The data suggest the population proportion is not significantly smaller than 50% at αα = 0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 50%.
- The data suggest the population proportion is not significantly smaller than 50% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 50%.
Interpret the p-value in the context of the study.
- There is a 20.27% chance that fewer than 50% of all voters prefer the Democratic candidate.
- If the population proportion of voters who prefer the Democratic candidate is 50% and if another 52 voters are surveyed then there would be a 20.27% chance fewer than 45% of the 52 voters surveyed prefer the Democratic candidate.
- If the sample proportion of voters who prefer the Democratic candidate is 45% and if another 52 voters are surveyed then there would be a 20.27% chance of concluding that fewer than 50% of all voters surveyed prefer the Democratic candidate.
- There is a 50% chance of a Type I error.
Interpret the level of significance in the context of the study.
- If the proportion of voters who prefer the Democratic candidate is smaller than 50% and if another 52 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 50%.
- There is a 5% chance that the proportion of voters who prefer the Democratic candidate is smaller than 50%.
- There is a 5% chance that the earth is flat and we never actually sent a man to the moon.
- If the population proportion of voters who prefer the Democratic candidate is 50% and if another 52 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 smaller than 50%

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Number of Potential voters (n) = 52

Number of voters who prefer democratic candidate (x) = 23

For this study, we will use z-test for a population proportion

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