Math Problem Statement

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 5.6 parts/million (ppm). A researcher believes that the current ozone level is not at the normal level. The mean of 8 samples is 5.4 ppm with a standard deviation of 0.9. Does the data support the claim at the 0.05level? Assume the population distribution is approximately normal.

Step 1 of 3 :

State the null and alternative hypotheses.

Solution

Step 1: State the Null and Alternative Hypotheses

We are conducting a hypothesis test to determine if the current ozone level differs from the normal level of 5.6 parts per million (ppm). The researcher suspects that the ozone level is not at the normal level, which indicates a two-tailed test.

  1. Null Hypothesis (H₀):
    The ozone level is equal to the normal level of 5.6 ppm.
    H0:μ=5.6H_0: \mu = 5.6

  2. Alternative Hypothesis (H₁):
    The ozone level is not equal to 5.6 ppm.
    H1:μ5.6H_1: \mu \neq 5.6

The test will proceed by comparing the sample data against these hypotheses.


Would you like details on how to proceed with the next steps of the hypothesis test? Feel free to ask any questions!

Related Questions:

  1. How is a two-tailed test different from a one-tailed test?
  2. What is the significance level (alpha) in hypothesis testing?
  3. How do you calculate the test statistic in a hypothesis test?
  4. What assumptions are necessary for using a t-test in this scenario?
  5. How does sample size affect the hypothesis test?

Tip: Always define whether your hypothesis test is one-tailed or two-tailed based on the research question before proceeding with calculations.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Two-tailed Test
Mean and Standard Deviation
T-distribution

Formulas

Null Hypothesis: H₀: μ = 5.6
Alternative Hypothesis: H₁: μ ≠ 5.6
Test Statistic Formula: t = (X̄ - μ) / (s / √n)

Theorems

Central Limit Theorem
Student's t-distribution

Suitable Grade Level

College-level Statistics