You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 53% at a level of significance of αα = 0.01. According to your sample, 58 out of 100 potential voters prefer the Democratic candidate. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean  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) The test statistic ? z t  = (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 Select an answer accept fail to reject reject the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly different from 53% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 53%. The data suggest the population proportion is not significantly different from 53% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 53%. The data suggest the populaton proportion is significantly different from 53% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 53%

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
icon
Related questions
Topic Video
Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 53% at a level of significance of αα = 0.01. According to your sample, 58 out of 100 potential voters prefer the Democratic candidate.

  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)
  1. The test statistic ? z t  = (please show your answer to 3 decimal places.)
  2. The p-value = (Please show your answer to 4 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 53% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 53%.
    • The data suggest the population proportion is not significantly different from 53% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 53%.
    • The data suggest the populaton proportion is significantly different from 53% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 53%
  6. Interpret the p-value in the context of the study.
    • There is a 31.64% chance that the percent of all voters who prefer the Democratic candidate differs from 53%.
    • If the sample proportion of voters who prefer the Democratic candidate is 58% and if another 100 voters are surveyed then there would be a 31.64% chance that we would conclude either fewer than 53% of all voters prefer the Democratic candidate or more than 53% of all voters prefer the Democratic candidate.
    • If the population proportion of voters who prefer the Democratic candidate is 53% and if another 100 voters are surveyed then there would be a 31.64% chance that either more than 58% of the 100 voters surveyed prefer the Democratic candidate or fewer than 48% of the 100 voters surveyed prefer the Democratic candidate.
    • There is a 31.64% chance of a Type I error.
  7. Interpret the level of significance in the context of the study.
    • If the proportion of voters who prefer the Democratic candidate is different from 53% and if another 100 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 53%.
    • There is a 1% chance that the proportion of voters who prefer the Democratic candidate is different from 53%.
    • If the population proportion of voters who prefer the Democratic candidate is 53% and if another 100 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 53%
    • There is a 1% chance that the earth is flat and we never actually sent a man to the moon.

 

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Proportions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL