Worksheet: Null Hypothesis Testing

In this worksheet, we will practice how to use hypothesis testing to assess a specific claim about the mean.

Q1:

A package of gum claims that the flavor lasts more than 39 minutes. What would the null hypothesis of a test to determine the validity of the claim be?

  • A𝐻>39
  • B𝐻<39
  • C𝐻39
  • D𝐻39
  • E𝐻=39

What sort of test is this?

  • ARight-tailed test
  • BTwo-sided test
  • CLeft-tailed test

Q2:

Suppose the average SAT score of graduating seniors is greater than 1,100. What are the null and alternative hypotheses?

  • A𝐻>1,100, 𝐻1,100
  • B𝐻=1,100, 𝐻>1,100
  • C𝐻1,100, 𝐻>1,100
  • D𝐻>1,100, 𝐻<1,100
  • E𝐻=1,100, 𝐻1,100

Q3:

Which of the following statements is not true for hypothesis testing?

  • AThe null hypothesis must contain the equal symbol.
  • BType II error is the probability of accepting false null hypothesis given that the alternative hypothesis is true.
  • CType I error is the probability of rejecting true null hypothesis.
  • DType II error is the probability of accepting false null hypothesis.

Q4:

Some teachers at a school say that high school juniors use computers for an average of 3.2 hours per day. The school principal wants to test if this is true. What are the null and alternative hypotheses?

  • A𝐻>3.2, 𝐻3.2
  • B𝐻<3.2, 𝐻3.2
  • C𝐻=3.2,𝐻3.2
  • D𝐻3.2,𝐻=3.2
  • E𝐻>3.2, 𝐻<3.2

Q5:

The school nurse thinks the average height of 7th graders has increased. The average height of a 7th grader five years ago was 145 cm with a standard deviation of 20 cm. She takes a random sample of 200 students and finds that the average height of her sample is 147 cm. What are the null and alternative hypotheses?

  • A𝐻𝜇145:, 𝐻𝜇>145:
  • B𝐻𝜇145:, 𝐻𝜇<145:
  • C𝐻𝜇<145:, 𝐻𝜇>145:
  • D𝐻𝜇=145:, 𝐻𝜇145:
  • E𝐻𝜇145:, 𝐻𝜇=145:

Conduct a single-tailed hypothesis test using a .05-significance level to test the null and alternative hypotheses. What is your conclusion?

  • AThere is insufficient evidence to reject the alternative hypothesis at the given significance level.
  • BThere is insufficient evidence to reject the null hypothesis at the given significance level.
  • CThere is sufficient evidence to reject the null hypothesis at the given significance level.

Are 7th graders now taller than they were before?

  • AYes
  • BNo

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