1) A news article that you read stated that 57% of voters prefer the Democratic candidate. You think that the actual percent is smaller. 134 of the 243 voters that you surveyed said that they prefer the Democratic candidate. What can be concluded at the 0.01 level of significance?

For this study, we should use Select an answer z-test for a population t-test for a population mean

The null and alternative hypotheses would be:

a. Ho:?μ p  Select an answer < = ≠ > ( )   (please enter a decimal)

b. H₁:?μ p  Select an answer = > < ≠ ( )   (Please enter a decimal)

c. The test statistic ? t z  = ( )  (please show your answer to 3 decimal places.)

d. The p-value = ( )  (Please show your answer to 4 decimal places.)

e. The p-value is ? > ≤ α

f. Based on this, we should Select an answer reject, fail to reject, accept the null hypothesis.

g. Thus, the final conclusion is that ...

The data suggest the population proportion is not significantly smaller 57% at α = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 57%.

The data suggest the population proportion is not significantly smaller 57% at α = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller 57%.

The data suggest the population proportion is significantly smaller 57% at α = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller 57%

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

There is a 57% chance of a Type I error.

If the sample proportion of voters who prefer the Democratic candidate is 55% and if another 243 voters are surveyed then there would be a 27.95% chance of concluding that fewer than 57% of all voters surveyed prefer the Democratic candidate.

If the population proportion of voters who prefer the Democratic candidate is 57% and if another 243 voters are surveyed then there would be a 27.95% chance fewer than 55% of the 243 voters surveyed prefer the Democratic candidate.

There is a 27.95% chance that fewer than 57% of all voters prefer the Democratic candidate.

i. 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 smaller 57%.

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 57% and if another 243 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 57%

If the proportion of voters who prefer the Democratic candidate is smaller 57% and if another 243 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 57%.

2. 12% of all college students volunteer their time. Is the percentage of college students who are volunteers different for students receiving financial aid? Of the 367 randomly selected students who receive financial aid, 37 of them volunteered their time. What can be concluded at the α = 0.10 level of significance?

a. For this study, we should use Select an answer z-test for a population, t-test for a population mean

b. The null and alternative hypotheses would be:

Ho:? p μ  Select an answer > = < ≠ ( )   (please enter a decimal)

H1:? μ p   Select an answer < = > ≠ ( )  (Please enter a decimal)

c. The test statistic ? t z = ( )  (please show your answer to 3 decimal places.)

d. The p-value =( ) (Please show your answer to 4 decimal places.)

e. The p-value is ? ≤ > α

f. Based on this, we should Select an answer accept, reject, fail to reject the null hypothesis.

g. Thus, the final conclusion is that ...

The data suggest the population proportion is significantly different from 12% at α = 0.10, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is different from 12%.

The data suggest the population proportion is not significantly different from 12% at α = 0.10, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is different from 12%.

The data suggest the population proportion is not significantly different from 12% at α = 0.10, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 12%.

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