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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.
Suppose the average SAT score of graduating seniors is greater than 1,100. What are the null and alternative hypotheses?
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?
What sort of test is this?
- ARight-tailed test
- BTwo-sided test
- CLeft-tailed test
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.
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?
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?
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?
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.
True or False: Significant level is the probability of rejecting when is true.
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?
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.