Democratic candidate

A news article that you read stated that 60% of voters prefer the Democratic candidate. You think that the actual percent is different. 150 of the 235 voters that you surveyed said that they prefer the Democratic candidate. What can be concluded at the 0.10 level of significance?

  1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
  2. 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)
  3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
  4. The p-value =  (Please show your answer to 4 decimal places.)
  5. The p-value is ? > ≤  αα
  6. Based on this, we should Select an answer reject fail to reject accept  the null hypothesis.
  7. Thus, the final conclusion is that …
    • The data suggest the populaton proportion is significantly different 60% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different 60%
    • The data suggest the population proportion is not significantly different 60% at αα = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different 60%.
    • The data suggest the population proportion is not significantly different 60% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 60%.
  8. Interpret the p-value in the context of the study.
    • If the population proportion of voters who prefer the Democratic candidate is 60% and if another 235 voters are surveyed then there would be a 23.08% chance that either more than 64% of the 235 voters surveyed prefer the Democratic candidate or fewer than 56% of the 235 voters surveyed prefer the Democratic candidate.
    • There is a 23.08% chance that the percent of all voters who prefer the Democratic candidate differs from 60%.
    • If the sample proportion of voters who prefer the Democratic candidate is 64% and if another 235 voters are surveyed then there would be a 23.08% 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.
    • There is a 23.08% chance of a Type I error.
  9. Interpret the level of significance in the context of the study.
    • If the proportion of voters who prefer the Democratic candidate is different 60% and if another 235 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 60%.
    • If the population proportion of voters who prefer the Democratic candidate is 60% and if another 235 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 different 60%
    • There is a 10% chance that the earth is flat and we never actually sent a man to the moon.
    • There is a 10% chance that the proportion of voters who prefer the Democratic candidate is different 60%.

2.

Only about 14% of all people can wiggle their ears. Is this percent different for millionaires? Of the 373 millionaires surveyed, 60 could wiggle their ears. What can be concluded at the αα = 0.01 level of significance?

  1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
  2. The null and alternative hypotheses would be:

H0:H0:  ? p μ  Select an answer ≠ = < >   (please enter a decimal)

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

  1. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
  2. The p-value =  (Please show your answer to 3 decimal places.)
  3. The p-value is ? > ≤  αα
  4. Based on this, we should Select an answer accept fail to reject reject  the null hypothesis.
  5. Thus, the final conclusion is that …
    • The data suggest the population proportion is not significantly different from 14% at αα = 0.01, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 14%.
    • The data suggest the population proportion is not significantly different from 14% at αα = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 14%.
    • The data suggest the populaton proportion is significantly different from 14% at αα = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 14%.

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