Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 60% at a level of significance of α = 0.01. According to your sample, 48 out of 70 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 populaton proportion is significantly different from 60% at α = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 60% The data suggest the population proportion is not significantly different from 60% at α = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 60%. The data suggest the population proportion is not significantly different from 60% at α = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 60%. Interpret the p-value in the context of the study. If the sample proportion of voters who prefer the Democratic candidate is 68% and if another 70 voters are surveyed then there would be a 14.32% chance that we would conclude either fewer than 60% of all voters prefer the Democratic candidate or more than 60% of all voters prefer the Democratic candidate. If the population proportion of voters who prefer the Democratic candidate is 60% and if another 70 voters are surveyed then there would be a 14.32% chance that either more than 68% of the 70 voters surveyed prefer the Democratic candidate or fewer than 52% of the 70 voters surveyed prefer the Democratic candidate. There is a 14.32% chance of a Type I error. There is a 14.32% chance that the percent of all voters who prefer the Democratic candidate differs from 60%. Interpret the level of significance in the context of the study. There is a 1% chance that the proportion of voters who prefer the Democratic candidate is different from 60%. There is a 1% 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 60% and if another 70 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 different from 60% If the proportion of voters who prefer the Democratic candidate is different from 60% and if another 70 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 60%.

Answer 1

null Hypothesis:               Ho:   p		=	0.600
alternate Hypothesis:    Ha: p		≠	0.600

sample success x   =		48
sample size          n    =		70
std error   se =√(p*(1-p)/n) =		0.0586
sample proportion p̂ = x/n=		0.6857
test stat z =(p̂-p)/√(p(1-p)/n)=		1.464
p value                          =		0.1432

p value is greater than alpha

we should fail to reject the null hypothesis.

The data suggest the population proportion is not significantly different from 60% at α = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 60%

If the population proportion of voters who prefer the Democratic candidate is 60% and if another 70 voters are surveyed then there would be a 14.32% chance that either more than 68% of the 70 voters surveyed prefer the Democratic candidate or fewer than 52% of the 70 voters surveyed prefer the Democratic candidate.

If the population proportion of voters who prefer the Democratic candidate is 60% and if another 70 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 different from 60%