Get personalized and accurate responses to your questions with IDNLearn.com. Our Q&A platform offers detailed and trustworthy answers to ensure you have the information you need.
Sagot :
Using the z-distribution, the estimate for how much the drug will lower a typical patient's systolic blood pressure is:
[tex]46.6 \leq \mu \leq 48[/tex]
What is a z-distribution confidence interval?
The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
- [tex]\overline{x}[/tex] is the sample mean.
- z is the critical value.
- n is the sample size.
- [tex]\sigma[/tex] is the standard deviation for the population.
In this problem, we have a 80% confidence level, hence[tex]\alpha = 0.8[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.8}{2} = 0.9[/tex], so the critical value is z = 1.28.
The other parameters are given by:
[tex]\overline{x} = 47.3, \sigma = 15.9, n = 878[/tex]
Then the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 47.3 - 1.28\frac{15.9}{\sqrt{878}} = 46.6[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 47.3 + 1.28\frac{15.9}{\sqrt{878}} = 48[/tex]
Hence the interval is:
[tex]46.6 \leq \mu \leq 48[/tex]
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.
