56% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 119 of the 243 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of αα = 0.10? 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: ? μ p  Select an answer > ≠ < =  (please enter a decimal)     H1: ? μ p  Select an answer > = < ≠  (Please enter a decimal) The test statistic ? t z  = (please show your answer to 3 decimal places.)

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56% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 119 of the 243 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of αα = 0.10?

  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: ? μ p  Select an answer > ≠ < =  (please enter a decimal)   
     H1: ? μ p  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 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 populaton proportion is significantly smaller than 56% at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is smaller than 56%
    • The data suggest the population proportion is not significantly smaller than 56% at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is equal to 56%.
    • The data suggest the population proportion is not significantly smaller than 56% at αα = 0.10, so there is not sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is smaller than 56%.
  6. Interpret the p-value in the context of the study.
    • There is a 1.36% chance that fewer than 56% of all students who played intramural sports graduate within six years.
    • If the sample proportion of students who played intramural sports who received a degree within six years is 49% and if another 243 such students are surveyed then there would be a 1.36% chance of concluding that fewer than 56% of all students who played intramural sports received a degree within six years.
    • There is a 56% chance of a Type I error.
    • If the population proportion of students who played intramural sports who received a degree within six years is 56% and if another 243 students who played intramural sports are surveyed then there would be a 1.36% chance fewer than 49% of the 243 students surveyed received a degree within six years.
  7. Interpret the level of significance in the context of the study.
    • If the population proportion of students who played intramural sports who received a degree within six years is smaller than 56% and if another 243 students who played intramural sports are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of all students who played intramural sports who received a degree within six years is equal to 56%.
    • There is a 10% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.
    • There is a 10% chance that the proportion of all students who played intramural sports who received a degree within six years is smaller than 56%.
    • If the population proportion of students who played intramural sports who received a degree within six years is 56% and if another 243 students who played intramural sports are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of all students who played intramural sports who received a degree within six years is smaller than 56%

 

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