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Let μ be the radiation level to which a radiation worker is exposed during the course of a year. The Environmental Protection Agency has set the maximum safe level of exposure at 6 rem per year. If a hypothesis test is to be performed to determine whether a workplace is safe, which is the most appropriate null hypothesis: H0 : μ ≤ 6.00, H0 : μ ≥ 6.00, or H0 : μ = 6.00? Explain.

Answer :

In hypothesis testing, the null hypothesis (denoted as [tex]H_0[/tex]) represents a statement of no effect or no difference, and it is the assumption that is initially assumed to be true. When assessing safety regarding radiation exposure, we are concerned about whether the radiation levels exceed the maximum safe level set by the Environmental Protection Agency (EPA), which is 6 rem per year.

To determine whether a workplace is safe, we set up a hypothesis test to assess if the radiation level, denoted by [tex]\mu[/tex], is greater than the safe level. This is primarily a problem of safety, because exceeding the safe level is of primary concern.

Here are the options for the null hypothesis:


  1. [tex]H_0: \mu \leq 6.00[/tex]

  2. [tex]H_0: \mu \geq 6.00[/tex]

  3. [tex]H_0: \mu = 6.00[/tex]


Given that we are interested in confirming if a workplace is safe, the null hypothesis should assume the condition that needs to be tested against. In this scenario, the most appropriate null hypothesis is:

[tex]H_0: \mu \leq 6.00[/tex]

Explanation:


  • Why [tex]H_0: \mu \leq 6.00[/tex] is appropriate:


    • This hypothesis assumes that the radiation levels are at a safe level or below (6 rem per year). If data collected shows that it significantly exceeds this level, we would reject the null hypothesis, suggesting that the workplace might not be safe.



  • Why the other options are not as suitable:


    • [tex]H_0: \mu \geq 6.00[/tex]: This would assume that the radiation levels are already at or above 6 rem, which does not align with testing for increased safety concerns.

    • [tex]H_0: \mu = 6.00[/tex]: This assumes the level is exactly 6 rem, which does not adequately account for cases where it could be either below or above this threshold in terms of safety considerations.




Therefore, for standard safety testing purposes with a concern against exposure higher than safe limits, [tex]H_0: \mu \leq 6.00[/tex] is the most suitable hypothesis to start testing from.

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