Hypothesis Test for Proportion

This is the same write-up as found in the previous question:

A recent newspaper article claimed that the President’s approval rating is 46%; however, a sample of 80 U.S. citizens shows that 43 of them approve of the President’s performance. At a 0.10 level of significance, you are interested in determining if there is evidence that the President’s approval rating is actually higher.

What is the p-value for this hypothesis test?

• .082

• .164

• .702

• .298

Sally reads a newspaper report claiming that 12% of all adults in the U.S. are left-handed. She decides to test this claim. Sally selects a random sample of 55 classmates and finds that 9 were left-handed. Does this provide sufficient evidence that the proportion of lefties in Sally’s school is different than the national figure? Use α = 0.01.

• 0.160

• 0.319

• 0.508

• 0.492

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

• Ho: μ > 21

  Ha: μ < 21

• Ho: p > .20

  Ha: p < .20

• Ho: p < .21

  Ha: p > .21

• Ho: p > .21

  Ha: p < .21

A mayor is concerned about the percentage of city residents who express disapproval of his job performance.  His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%.  They will use a follow up poll to access effectiveness.  What are the correct null and alternative hypotheses?

• Ho: p=.21
  Ha: p > .21

• Ho: p< .21
  Ha: p= .21

• Ho: p> .21
  Ha: p= .21

• Ho: p= .21
  Ha: p< .21

Elsie bought a new bowling ball. She suspects that she'll roll a strike in a larger percentage of rolls with her new ball than her old ball. She takes a sample of 50 rolls with each ball to test if she rolls a strike significantly more often with the new ball.

Which of the following is an appropriate set of hypotheses for Elsie's significance test?

• 
• 
• 
• 

If the difference of two proportions (p₁-p₂) shows a confidence interval of (-0.13, 0.32), what would have been our decision from the 2-prop z-test?

• Fail to reject Ha since 0 is in the interval

• Fail to reject Ho since 0 is in the interval

• Reject Ho since 0 is in the interval

• Reject Ha since 0 is in the interval

Kiley has a dime and a nickel, and she wonders if they have the same likelihood of showing heads when they are flipped. She flips each coin 100 times to test if there is a significant difference in the proportion of flips that they each land showing heads.

Which of the following is an appropriate set of hypotheses for Kiley's significance test?

• 
• 
• 
• 

5% of trucks of a certain model have needed new engines after being driven between 0 and 100 miles.  The manufacturer hopes that the redesign of one of the engine's components has solved this problem.  Write the null and alternative hypotheses for this situation.

• Ho:  p< 0.05
  Ha:  p = 0.05

• Ho:  p = 0.05
  Ha:  p > 0.05

• Ho:  p = 0.05
  Ha:  p < 0.05

• Ho:  p > 0.05
  Ha:  p = 0.05

A state university wants to increase it retention rate of 4% for graduating students from the previous year.  After implementing several new programs during the last two years, the university reevaluates it retention rate and comes up with a P-value of 0.075.  What is a reasonable conclusion?

• There is a92.5% chance of the new programs having no effect on retention.

• There is a 7.5% chance of the new programs having no effect on retention.

• We can say there is a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation.  There is no evidence the new programs are more effective, but we cannot conclude that they have no effect on retention.

• There's only a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation.  We conclude the new programs are more effective.

A state university wants to increase its retention rate of 4% for graduating students from the previous year.  After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%.  Test the appropriate hypothesis and state your conclusion.  Be sure to check assumptions and conditions.

• Ho:  p = .04; Ha: p> .04; z = 0.96; P-value = 0.1685.  This data does not show that more than 4% of students are retained; they should not continue with the new programs.

• Ho:  p = .04; Ha: p<.04; z = -1.07; P-value =0.8577.  This data shows that more than 4% of the students are retained; the university should continue with the new programs.

• Ho: p = .04; Ha: p ≠ .04; z = 1.07; P-value = 0.2846;  This data does not show that more than 4% of students are retained; the university should not continue with the new programs.