Hypothesis Test AP Stat

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 nationwide poll recently showed an unemployment rate of 9% in the US. The mayor of a local town wonders if this is true for her town, so she plans to take a sample of residents to see if the unemployment rate is significantly different than 9% in her town. Here are the hypotheses:
H_0: p e0.09
H_a: p e0.09
Which of the following would be a type I error?

• She concludes the town's unemployment rate is not 9% when it actually is.

• She concludes the town's unemployment rate is not 9% when it actually is not.
  

• She concludes the town's unemployment rate is 9% when it actually is.
  

• She concludes the town's unemployment rate is 9% when it actually is not.
  

A large nationwide poll recently showed an unemployment rate of 9% in the US. The mayor of a local town wonders if this is true for her town, so she plans to take a sample of residents to see if the unemployment rate is significantly different than 9% in her town. Here are the hypotheses:
H_0: p e0.09
H_a: p e0.09
Which of the following would be a type II error?

• She concludes the town's unemployment rate is not 9% when it actually is.

• She concludes the town's unemployment rate is not 9% when it actually is not.
  

• She concludes the town's unemployment rate is 9% when it actually is.
  

• She concludes the town's unemployment rate is 9% when it actually is not.
  

• They don't consider building the new cafeteria when they should.

• They don't consider building a new cafeteria when they shouldn't.
  

• They consider building a new cafeteria when they shouldn't.
  

• They consider building a new cafteria when they should.
  

• The soil is actually safe and construction continues

• The soil is actually safe and construction stops

• The soil is actually unsafe and construction continues

• The soil is actually unsafe and construction stops

Regulations from the EPA say that soil used in playgrounds should not have lead levels more than 400 ppm. Before beginning construction on a new site, a sample of soil is taken and tested. If the mean level of lead in this soil is significantly higher than 400 ppm, then construction cannot continue. Here are the hypotheses:
H_0: \mu = 400 ppm H_a: \mu > 400 ppm 
Which of the following would be a type I error?

• The soil is actually safe and construction continues

• The soil is actually safe and construction stops

• The soil is actually unsafe and construction continues

• The soil is actually unsafe and construction stops

What is the probability of making a Type I error?

• alpha

• 1 minus the probability of a Type II error

• 1 minus the power

• the p-value

What is the probability of making a Type II error?

• alpha

• 1 minus the probability of a Type I error

• 1 minus the power

• the p-value

Assuming the conditions for inference were met, which of the following is the most appropriate conclusion to draw at the α = 0.05 level?

• The test provides convincing evidence that the carbohydrate content of variety 1 is higher

  than variety 2.

• The test provides convincing evidence that the carbohydrate contents of the two varieties

  are equal.

• We accept Ha: variety 1 has a higher carbohydrate content than variety 2.

• We reject Ho: variety 1 has a higher carbohydrate content than variety 2.

• We cannot reject Ho: we do not have convincing evidence that the carbohydrate contents

  are different.

Janice and her cousin Linda are a little competitive about the relative merits of their home towns. One contest they had was to determine who had more rainy days. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Asheville, and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Lincoln. They intend to perform a test of significance on their data, using the hypotheses Ho : pA − pL = 0 versus Ha : pA − pL ≠ 0 and the 0.05 significance level. When calculating the test statistic, what expression would they use to estimate the standard deviation of the sampling distribution of the difference in proportions?