1. Identifying Hypotheses
  2. Computing P-Values (Without Context)
  3. Conceptual Question

 

 

Identifying Hypotheses

For each research hypothesis or statement below, construct the null and alternative hypotheses (use their respective symbols) and explicitly define the parameter in the hypotheses.

  1. A researcher is investigating the mean growth of a certain cactus under a variety of environmental conditions. Under the current environmental conditions, he hypothesizes that mean growth is no more than 4 cm.
  2. Machowiak et al. (1992) critically examined the belief that the mean body temperature differed from 98.6oF by measuring the body temperatures of 93 healthy humans.
  3. A study by Cheshire et al. (1994) reported on six patients with chronic myofascial pain syndrome. The authors were examining the hypothesis that the mean pain length was greater than 2.5 years.

 

I urge you to follow these steps when answering all p-value-related questions:
  1. Identify H0 and HA. If the question has a context then the parameter should be stated within that context.
  2. Define the p-value specific to the situation.
  3. Draw the null distribution.
  4. Compute the p-value.
  5. Make a decision about H0. If the question has a context then the conclusion should be stated within that context.
A reminder to use these steps will NOT be provided on future quizzes, but you should get in the habit of following them. See here for a demonstration of the steps.

 

Computing P-Values (without context)

Compute the p-value (see the steps suggested above) For each situation below.

  1. HA: μ>880, σ=90, n=80, x̄=918, α=0.01.
  2. HA: μ≠800, σ=60, n=25, x̄=824, α=0.01.
  3. α=0.05, HA: μ<80, n=30, σ=20, x̄=73.
  4. α=0.05, HA: μ≠1500, n=40, σ=800, x̄=1370.
  5. α=0.10, HA: μ>10, n=25, σ=5, x̄=12.1.
  6. α=0.05, HA: μ<50, n=50, σ=20, x̄=43.8.
  7. α=0.01, HA: μ≠100, n=100, σ=15, x̄=98.

Conceptual Question

Describe why we must formally go through the steps of a hypothesis test to conclude that μ>11 when we observe x̄=12.1.