Answer:
95% confidence interval for the true mean weight of men is [127.71 pounds , 172.30 pounds].
Step-by-step explanation:
We are given that the average weight of a man from the sample was found to be 150 pounds with a standard deviation of 54 pounds
25 men from Pinellas County were randomly drawn from a population of 100,000 men.
Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;
P.Q. = ~
where, = sample average weight of a man = 150 pounds
s = sample standard deviation = 54 pounds
n = sample of men = 25
<em>Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>
So, 95% confidence interval for the true mean, is ;
P(-2.064 < < 2.064) = 0.95 {As the critical value of t at 24 degree of
freedom are -2.064 & 2.064 with P = 2.5%}
P(-2.064 < < 2.064) = 0.95
P( < < ) = 0.95
P( < < ) = 0.95
<u>95% confidence interval for </u> = [ , ]
= [ , ]
= [127.71 pounds , 172.30 pounds]
Therefore, 95% confidence interval for the true mean weight of men is [127.71 pounds , 172.30 pounds].