1 prop z test

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

• a) Reject the null hypothesis

• b) Reject the alternative hypothesis

• c) Fail to reject the null hypothesis

• d) Fail to reject the alternative hypothesis

When p-value is greater than alpha we:

• Reject Ho

• Fail to reject Ha

• Fail to reject Ho

• Reject Ha

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

Lumber companies dry freshly cut wood in kilns before selling it. A certain percentage of boards develop cracks on their ends during drying. The current drying procedure is known to produce cracks in 16% of boards. The drying supervisor wants to try a new method that she believes will result in a proportion of cracked boards that is less than 16%.

Write the appropriate hypotheses.

• Ho: p = 0.16

  Ha: p = 0.16

• Ho: p = 0.16

  Ha: p =/= 0.16

• Ho: p = 0.16

  Ha: p > 0.16

• Ho: p = 0.16

  Ha: p < 0.16

• Since our p-value of 0.027 is >undefined , we fail to reject the null hypothesis. We do not have convincing evidence that the new method is better. 

A Gallup poll report revealed that 72% of teens said they rarely or never argue with their friends. Yvonne wonders if this result is true for her school. She surveys a random sample of 150 students and 64% of them say they rarely or never argue with friends. She uses the data to perform a test of Ho: p = 0.72 versus Ha: p=/= 0.72.

The test yields a p-value of 0.0291. What conclusion would you make for a significance level of 5%?

• Since our p-value of 0.0291 is more than 5%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

• Since our p-value of 0.0291 is less than 5%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

• Since our p-value of 0.0291 is more than 5%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

• Since our p-value of 0.0291 is less than 5%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

A Gallup poll report revealed that 72% of teens said they rarely or never argue with their friends. Yvonne wonders if this result is true for her school. She surveys a random sample of 150 students and 64% of them say they rarely or never argue with friends. She uses the data to perform a test of Ho: p = 0.72 versus Ha: p=/= 0.72.

The test yields a p-value of 0.0291. What conclusion would you make for a significance level of 1%?

• Since our p-value of 0.0291 is more than 1%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

• Since our p-value of 0.0291 is less than 1%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

• Since our p-value of 0.0291 is more than 1%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

• Since our p-value of 0.0291 is less than 1%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

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.  

• 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.