Respuesta :
Answer:
Correct formula for a 99% confidence interval for the population mean = [tex][xbar - 2.61138*\frac{480}{\sqrt{144} } , xbar + 2.61138*\frac{480}{\sqrt{144} }][/tex]
Step-by-step explanation:
We are provided a simple random sample of 144 items of which sample mean, xbar = 1250.25 and Standard Deviation, s = 480.
We know that [tex]\frac{xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] follows [tex]t_n_-_1[/tex] i.e.;
[tex]\frac{1250.25 - \mu}{\frac{480}{\sqrt{144} } }[/tex] follows [tex]t_1_4_3[/tex]
So, 99% confidence interval is given by ;
P(-2.61138 < [tex]t_1_4_3[/tex] < 2.61138) = 0.99 {because at 143 degree of freedom t table
gives critical value of 2.61138 at 0.5% level}
Now, after further solving this we get,
99% confidence interval for the population mean =
[tex][xbar - 2.61138*\frac{480}{\sqrt{144} } , xbar + 2.61138*\frac{480}{\sqrt{144} }][/tex]
Since, in the question options are not given so this must be the correct formula for calculating 99% confidence interval for the population mean.
