# 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?

• A,
• B,
• C,
• D,
• E,

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?

• A
• B
• C
• D
• E

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?

• A,
• B,
• C,
• D,
• E,

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?

• A,
• B,
• C,
• D,
• E,

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.

• A and
• B and
• C and
• D and
• E and

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 is the probability of rejecting when is true.

• AFalse
• BTrue

Q8:

The water temperature in a storeroom is normally distributed. The mean temperature should not exceed . The standard deviation of water temperature is . Measurements on 9 randomly selected days produce a mean of . 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.

• A
• B

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