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Agency leadership is very interested in trend analysis. Using the 750 randomly selected vehicles as their​ sample, data was collected to determine which vehicles currently meet or exceed fuel economy standards and which vehicles currently do not meet fuel economy standards. This information is found in the Meet or Not Meet Current Standards column. Agency leadership asks your team to construct a​ 95% One-Sample proportion confidence interval for the population proportion of all vehicles that meet current fuel economy standards. Assume that all necessary Central Limit Theorem conditions for a​ One-Proportion confidence interval have been met. What is the​ 95% lower​ limit?

Respuesta :

Using the z-distribution, as we are working with a proportion, considering that the estimate is of 90%, the 95% lower​ limit is of 0.8785.

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

  • [tex]\pi[/tex] is the sample proportion.
  • z is the critical value.
  • n is the sample size.

In this problem, we have that:

  • There is a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
  • We suppose an estimate of [tex]\pi = 0.9[/tex].
  • The sample size is of n = 750.

Hence, the lower bound of the interval will be given by:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 1.96\sqrt{\frac{0.9(0.1)}{750}} = 0.8785[/tex]

More can be learned about the z-distribution at https://brainly.com/question/25890103

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