Answer to Question #121964 in Statistics and Probability for Shanzay

Question

A firm wants to estimate mean lifetime of a tool.From previous experiments it is known that lifetimes are normally distributed.It draws a random sample of four of these tools and finds that there lifetimes are 9.3,7.9,10.8and 11.4.Calculate a 95% cinfidence interval for mean lifetime of that kind of tool

Answer 1

To find : confidence interval for 95%

Since population sd is unknown and it is normally distributed , we use t confidence interval

Formula:

$\left [\overline{x } -t^{^{*}}\frac{s}{\sqrt{n}},\overline{x } +t^{^{*}}\frac{s}{\sqrt{n}}\right ]$

From given data

$\overline{x }= 9.85, s=1.572,t^{*}=$ 3.182

(The number of degrees of freedom are df = 4 - 1 = 3 and the significance level is alpha = 0.05)

calculation:

${\left [9.85 -3.182*\frac{1.572}{\sqrt{4}},9.85 +3.182*\frac{1.572}{\sqrt{4}}\right ]}$

[7.349,12.351] is the required solution.