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Two researchers, Justin and Henry, work together to study what proportion of subjects have a certain genotype in the population. They each collect a simple random sample and they find that the sample proportion is 0.70. When they construct a confidence interval based on this sample proportion, Henry comes up with (0.632, 0.768) while Justin gets (0.652, 0.788). Indicate which interval has to be wrong and why.

Respuesta :

Using confidence interval concepts, it is found that Justin is wrong, as his interval is not symmetric about the sample proportion of 0.7.

  • A confidence interval has two bounds, a lower bound and an upper bound.
  • A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
  • The margin of error is the difference between the two bounds, divided by 2.

In this problem, the point estimate is of 0.7.

  • Henry's interval is symmetric, as [tex]0.768 - 0.7 = 0.7 - 0.632[/tex].
  • Justin's is not, as [tex]0.788 - 0.7 \neq 0.7 - 0.652[/tex].

Hence, Justin is wrong, as his interval is not symmetric about the sample proportion of 0.7.

For more on confidence intervals, you can check https://brainly.com/question/25822483

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