You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 76% at a level of significance of αα = 0.01. According to your sample, 42 out of 60 potential voters prefer the Democratic candidate. For this study, we should use The null and alternative hypotheses would be: Ho: (please enter a decimal) H1: (Please enter a decimal) The test statistic = (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 the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton proportion is significantly smaller than 76% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 76% The data suggest the population proportion is not significantly smaller than 76% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 76%. The data suggest the population proportion is not significantly smaller than 76% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 76%.

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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Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 76% at a level of significance of αα = 0.01. According to your sample, 42 out of 60 potential voters prefer the Democratic candidate.

For this study, we should use
The null and alternative hypotheses would be:
Ho: (please enter a decimal)
H₁: (Please enter a decimal)

The test statistic = (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 the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the populaton proportion is significantly smaller than 76% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 76%
- The data suggest the population proportion is not significantly smaller than 76% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 76%.
- The data suggest the population proportion is not significantly smaller than 76% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 76%.
Interpret the p-value in the context of the study.
- If the sample proportion of voters who prefer the Democratic candidate is 70% and if another 60 voters are surveyed then there would be a 13.83% chance of concluding that fewer than 76% of all voters surveyed prefer the Democratic candidate.
- If the population proportion of voters who prefer the Democratic candidate is 76% and if another 60 voters are surveyed then there would be a 13.83% chance fewer than 70% of the 60 voters surveyed prefer the Democratic candidate.
- There is a 13.83% chance that fewer than 76% of all voters prefer the Democratic candidate.
- There is a 76% 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 76% and if another 60 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 76%.
- There is a 1% chance that the earth is flat and we never actually sent a man to the moon.
- There is a 1% chance that the proportion of voters who prefer the Democratic candidate is smaller than 76%.
- If the population proportion of voters who prefer the Democratic candidate is 76% and if another 60 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is smaller than 76%