Answer:
95% two-sided confidence interval for the true mean heights of men is [168.8 cm , 181.2 cm].
Step-by-step explanation:
We are given that the heights of 40 randomly chosen men are measured and found to follow a normal distribution.
An average height of 175 cm is obtained. The standard deviation of men's heights is 20 cm.
Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;
P.Q. = ~ N(0,1)
where, = sample average height = 175 cm
= population standard deviation = 20 cm
n = sample of men = 40
<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>
So, 95% confidence interval for the true mean, is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%
level of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for </u> = [
,
]
= [ ,
]
= [168.8 cm , 181.2 cm]
Therefore, 95% confidence interval for the true mean height of men is [168.8 cm , 181.2 cm].
<em>The interpretation of the above interval is that we are 95% confident that the true mean height of men will be between 168.8 cm and 181.2 cm.</em>