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Sagot :
a) 92% Confidence interval: (1027.5,1048.5)
b) Sample size = 100
What is Sample size?
The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.
We are given the following in the question:
Sample mean, = 1038
Sample size, n = 25
Alpha, α = 0.08
Population standard deviation, σ = 30
a) 92% Confidence interval:
[tex]$\mu \pm z_{\text {critical }} \frac{\sigma}{\sqrt{n}}$[/tex]
Putting the values, we get,
[tex]$z_{\text {critical }}$[/tex] at [tex]$\alpha_{0.08}=\pm 1.75$[/tex]
[tex]$1038 \pm 1.75\left(\frac{30}{\sqrt{25}}\right)=1038 \pm 10.5=(1027.5,1048.5)$[/tex]
b) In order to reduce the confidence interval by half, we have to quadruple the sample size.
Thus,
Sample size [tex]$=25 \times 4=100$[/tex]
To learn more about Sample mean visit:https://brainly.com/question/14127076
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