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Martha Stewart has developed a new perfume. She decides to test its side effects by spraying the perfume in 31 randomly chosen houses. She records the level of antigens that create an allergic response. If the antigen level is high enough, the person will go into anaphylactic shock. The mean of her sample is a lot bigger than the median, but Martha hopes that a 90% confidence interval will contain zero. Her confidence interval is (0.116, 1.884). Disappointed, she offers you $144 to find an acceptable, realistic way to change the confidence interval to contain zero. What could you say to earn the money

Respuesta :

The acceptable and realistic ways to to change the confidence interval to contain zero are;

  • Martha should decrease x-bar by providing medicine to treat shock to the perfume users.
  • Decrease sample size than 30
  • Increase the confidence level, till the interval contains zero

Reasons:

The confidence interval is given by the following formula;

[tex]CI=\bar{x}\pm t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex]

When the mean, [tex]\overline x[/tex], is positive and large, both values, [tex]\bar{x}+ t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and [tex]\bar{x} -t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], will be positive.

Therefore, Martha has to either intervene to reduce the mean also known as x-bar

Increasing the confidence level will increase the allowable error such that [tex]\bar{x} < t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and the interval will contain zero

Therefore;

  • Martha should decrease x-bar, [tex]\overline x[/tex], by providing medicine to treat shock to the perfume users
  • Use a much smaller sample size, n, such that [tex]t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}} > \bar{x}[/tex]

  • Increase the confidence level to 95% or 99%, thereby increasing the error bound

Learn more here:

https://brainly.com/question/13034570

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