Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 58% at a level of significance of α = 0.10. According to your sample, 43 out of 73 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 α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly larger than 58% at α = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 58%. The data suggest the population proportion is significantly larger than 58% at α = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 58% The data suggest the population proportion is not significantly larger than 58% at α = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 58%. Interpret the p-value in the context of the study. There is a 43.78% chance of a Type I error. If the population proportion of voters who prefer the Democratic candidate is 58% and if another 73 voters are surveyed then there would be a 43.78% chance that more than 59% of the 73 voters surveyed prefer the Democratic candidate. If the sample proportion of voters who prefer the Democratic candidate is 59% and if another 73 voters are surveyed then there would be a 43.78% chance of concluding that more than 58% of all voters surveyed prefer the Democratic candidate. There is a 43.78% chance that more than 58% of all voters prefer the Democratic candidate. Interpret the level of significance in the context of the study. If the population proportion of voters who prefer the Democratic candidate is 58% and if another 73 voters are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is larger than 58% There is a 10% chance that the earth is flat and we never actually sent a man to the moon. If the proportion of voters who prefer the Democratic candidate is larger than 58% and if another 73 voters are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 58%. There is a 10% chance that the proportion of voters who prefer the Democratic candidate is larger than 58%.

Answer 1

n = 73

x = 43

p̄ = x/n = 0.5890

α = 0.1

Null and Alternative hypothesis:

Ho : p = 0.58

H1 : p > 0.58

Test statistic:

z = (p̄ -p)/√(p*(1-p)/n) = (0.589 - 0.58)/√(0.58 * 0.42/73) = 0.157

p-value = 1- NORM.S.DIST(0.1565, 1) = 0.4378

Decision:

p-value > α, Do not reject the null hypothesis

Conclusion:

The data suggest the population proportion is not significantly larger than 58% at α = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 58%.

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Interpret the p-value in the context of the study.

If the population proportion of voters who prefer the Democratic candidate is 58% and if another 73 voters are surveyed then there would be a 43.78% chance that more than 59% of the 73 voters surveyed prefer the Democratic candidate.

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Interpret the level of significance in the context of the study.

There is a 10% chance that the proportion of voters who prefer the Democratic candidate is larger than 58%.