Statistics: Hypothesis Testing: Null and Alternate
Writing null and alternate hypotheses for claims
Statistics: Hypothesis Testing: Null and Alternate
Writing null and alternate hypotheses for claims
Statistics - Grade 9-12
- 1
A cereal company claims that the mean weight of cereal in its boxes is 18 ounces. Write the null and alternate hypotheses to test whether the true mean weight is different from 18 ounces.
The phrase different from means a two-sided test.
Let μ be the true mean weight of cereal in the boxes. The null hypothesis is H0: μ = 18, and the alternate hypothesis is Ha: μ ≠ 18. - 2
A school counselor believes that more than 60% of students at the school participate in at least one extracurricular activity. Write the null and alternate hypotheses.
Let p be the true proportion of students who participate in at least one extracurricular activity. The null hypothesis is H0: p = 0.60, and the alternate hypothesis is Ha: p > 0.60. - 3
A battery manufacturer states that its batteries last an average of at least 10 hours. A consumer group wants to test whether the batteries last less than 10 hours on average. Write the null and alternate hypotheses.
The consumer group is looking for evidence that the mean is lower than the stated value.
Let μ be the true mean battery life in hours. The null hypothesis is H0: μ = 10, and the alternate hypothesis is Ha: μ < 10. - 4
A restaurant owner says that the average wait time for a table is 15 minutes. A manager collects data to see if the average wait time has changed. Write the null and alternate hypotheses.
Let μ be the true mean wait time in minutes. The null hypothesis is H0: μ = 15, and the alternate hypothesis is Ha: μ ≠ 15. - 5
A researcher is testing whether a new study app increases the average test score above the usual mean of 82 points. Write the null and alternate hypotheses.
The word increases points to a greater-than alternate hypothesis.
Let μ be the true mean test score for students using the study app. The null hypothesis is H0: μ = 82, and the alternate hypothesis is Ha: μ > 82. - 6
A city reports that 35% of households recycle weekly. An environmental group wants to know if the actual proportion is not 35%. Write the null and alternate hypotheses.
Let p be the true proportion of households that recycle weekly. The null hypothesis is H0: p = 0.35, and the alternate hypothesis is Ha: p ≠ 0.35. - 7
For the hypotheses H0: μ = 120 and Ha: μ < 120, state whether the test is left-tailed, right-tailed, or two-tailed. Explain your answer.
Look only at the direction of the alternate hypothesis.
The test is left-tailed because the alternate hypothesis uses the less-than symbol, which looks for values below 120. - 8
For the hypotheses H0: p = 0.25 and Ha: p > 0.25, describe the claim being tested in words.
The test is checking whether the true proportion is greater than 0.25, or greater than 25%. - 9
A student writes H0: x̄ = 50 and Ha: x̄ ≠ 50 to test a claim about a population mean. Identify the mistake and correct the hypotheses.
Hypotheses are written about population parameters, not sample statistics.
The mistake is using the sample mean x̄ instead of the population mean μ in the hypotheses. The correct hypotheses are H0: μ = 50 and Ha: μ ≠ 50. - 10
A company wants to test whether fewer than 5% of its packages arrive late. Write the null and alternate hypotheses.
Let p be the true proportion of packages that arrive late. The null hypothesis is H0: p = 0.05, and the alternate hypothesis is Ha: p < 0.05. - 11
Choose the correct alternate hypothesis for this situation: A coach wants to test whether the average mile time of runners is lower than 7 minutes. Options: Ha: μ = 7, Ha: μ < 7, Ha: μ > 7, Ha: μ ≠ 7.
Lower than means less than.
The correct alternate hypothesis is Ha: μ < 7 because the coach is testing whether the average mile time is lower than 7 minutes. - 12
A news article says that the average daily screen time for teens is 7.5 hours. A researcher thinks the true average is different. Write the null hypothesis, the alternate hypothesis, and identify the type of test.
Let μ be the true mean daily screen time for teens in hours. The null hypothesis is H0: μ = 7.5, and the alternate hypothesis is Ha: μ ≠ 7.5. This is a two-tailed test because the researcher is testing for a difference in either direction.