Population Proportion

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

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 company hopes to improve its engines, setting a goal of no more than 3% of customers using their warranty on defective engine parts.  A random survey of 1200 customers found only 20 with complaints.  Create a 95% confidence interval for the true level of warranty users among all customers.

• Based on the data we are 95% confident the proportion of warranty users is between 0.9% and 2.4%.  Therefore the company met its goal.
• Based on the data we are 95% confident the proportion of warranty users is between 2.0% and 2.4%.  Therefore the company has met its goal.
• Based on the data we are 95% confident the proportion of warranty users is between 0.9% and 3.8%.  therefore, the company has not met its goal.
• Based on the data we are 95% confident the proportion of warranty users is between 0% and 2.4%.  Therefore, the company has met its goal.

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.

The probability of observing a value for a test statistic at least as far from the hypothesized value as the statistic value actually observed if the null hypothesis is true

• P-Hat
• One-Proportion z-test
• Z*
• P-Value

A Type I error is when: 

• We obtain the wrong test statistic
• We reject the null hypothesis when it is actually true
• We fail to reject the null hypothesis when it's actually false
• We reject the alternate hypothesis when it's actually true