Hypothesis Test 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 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

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

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

A large-scale study found that 42% of Americans play video games. A random sample of 1100 teenagers were asked whether they play games online; 575 said they did. Is there sufficient evidence to suggest that the proportion of teens who play video games is different from the national figure? Use a 5% level of significance.

Which is the correct p-value for this test?

• 5.08 x 10 ^-12

• 2.84 x 10 ^-91

• 2.56 x 10 ^-12

• 0

A large-scale study found that 42% of Americans play video games. A random sample of 1100 teenagers were asked whether they play games online; 575 said they did. Is there sufficient evidence to suggest that the proportion of teens who play video games is different from the national figure? Use a 5% level of significance.

Which is the correct conclusion for this test?

• Snice p-value = 5.08 x 10 ^-12 < 0.05, I reject H0. There is enough evidence to suggest a difference.

• Snice p-value = 5.08 x 10 ^-12 < 0.05, I fail to reject H0. There is enough evidence to suggest a difference.

• Snice p-value = 5.08 > 0.05, I fail to reject H0. There is not enough evidence to suggest a difference.

• Snice p-value = 5.08 > 0.05, I reject H0. There is enough evidence to suggest a difference.

A nationwide survey of 1500 adults asked about attitudes toward “alternative medicine” such as acupuncture, massage therapy, etc. Among the 1500 respondents, 660 said they would use alternative medicine if traditional medicine was not producing the results they wanted. Do these data provide enough evidence to suggest that less than half of all adults would use alternative medicine if traditional medicine didn’t produce their desired results? Use a 5% level of significance.

Which is the correct p-value for this test?

• 0.002

• 0.999

• 0.500

• 0.000