# Lesson Worksheet: Introduction to Hypothesis Testing Mathematics

In this worksheet, we will practice using hypothesis testing to assess claims about population parameters.

**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 manufacturerβs 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

**Q10: **

A machine produces rods used in car engines. A random sample of 25 rods is selected and their diameters are measured. The resulting mean and standard deviation are 7.212 and 0.005 respectively. Test the hypotheses and at a significant level of 0.01.

- A
- B