Hypothesis Test for a 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

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

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

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

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.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

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.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

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.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

A P-value indicates:

• the probability that the null hypothesis is true
• the probability that the alternative hypothesis is true
• the probability of the observed statistic given the null hypothesis is true
• the probability that the null is true given the observed statistic

Proposes what we should conclude if we find the null hypothesis to be unlikely

• Null Hypothesis
• Alternative Hypothesis
• Assumptions & Conditions
• P-Hat

The claim being assessed in a hypothesis test

• Null hypothesis
• Alternative hypothesis
• P-Value
• Parameter

Tags

CCSS.HSS.IC.B.5

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

Tags

CCSS.HSS.IC.B.5

CCSS.HSS.ID.A.4

Which of the following is the FIRST step of a hypothesis test?

• Check assumptions & conditions
• Find your test statistic
• State your conclusion
• State your null & alternative hypotheses