Lesson Worksheet: Null Hypothesis Testing Mathematics

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

Q1:

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

  • A𝐻>1,100, 𝐻≀1,100
  • B𝐻=1,100, 𝐻>1,100
  • C𝐻≀1,100, 𝐻>1,100
  • D𝐻>1,100, 𝐻<1,100
  • E𝐻=1,100, 𝐻≠1,100

Q2:

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
  • C𝐻≀39
  • D𝐻β‰₯39
  • E𝐻=39

What sort of test is this?

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

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?

  • Aπ»βˆΆπ‘‘>3.2, π»βˆΆπ‘‘β‰ 3.2
  • Bπ»βˆΆπ‘‘<3.2, π»βˆΆπ‘‘β‰ 3.2
  • Cπ»βˆΆπ‘‘=3.2,π»βˆΆπ‘‘β‰ 3.2
  • Dπ»βˆΆπ‘‘β‰ 3.2,π»βˆΆπ‘‘=3.2
  • Eπ»βˆΆπ‘‘>3.2, π»βˆΆπ‘‘<3.2

Q5:

The school nurse thinks the average height of 7th graders has increased. The average height of a 7th grader 5 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?

  • Aπ»πœ‡β‰€145:, π»πœ‡>145:
  • Bπ»πœ‡β‰€145:, π»πœ‡<145:
  • Cπ»πœ‡<145:, π»πœ‡>145:
  • Dπ»πœ‡=145:, π»πœ‡β‰ 145:
  • Eπ»πœ‡β‰€145:, π»πœ‡=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

Q6:

A manufacturer specifies that the mean lifetime of a certain type of batteries is at least 273 hours. A sample of 49 batteries has an average lifetime of 270.5 hours and a standard deviation of 9 hours.

State the null and the alternative hypotheses.

  • Aπ»βˆΆπœ‡<273 and π»βˆΆπœ‡β‰₯273
  • Bπ»βˆΆπœ‡β‰₯273 and π»βˆΆπœ‡β‰€273
  • Cπ»βˆΆπœ‡>273 and π»βˆΆπœ‡<273
  • Dπ»βˆΆπœ‡β‰₯273 and π»βˆΆπœ‡>273
  • Eπ»βˆΆπœ‡β‰₯273 and π»βˆΆπœ‡<273

Test the manufacturer’s claim at the significance level of 0.05.

  • AThe claim fails to be rejected.
  • BThe claim is rejected.

Q7:

True or False: Significant level 𝛼 is the probability of rejecting 𝐻 when 𝐻 is true.

  • AFalse
  • BTrue

Q8:

The water temperature in a storeroom is normally distributed. The mean temperature should not exceed 100∘F. The standard deviation of water temperature is 2∘F. Measurements on 9 randomly selected days produce a mean of 101.5∘F. Should the water temperature be regarded as acceptable with a significant level of 0.05?

  • AYes
  • BNo

Q9:

A rod used in a machine application must have a diameter of 1.2 mm. A random sample of 25 rods produces a mean diameter of 1.194 cm. The diameter is known to be normally distributed with a standard deviation of 0.03 cm. Test this hypothesis with a significant level of 0.02.

  • AFailtoreject𝐻
  • BReject𝐻

This lesson includes 63 additional question variations for subscribers.

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