Answer:
98% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students is [0.56 inches , 6.04 inches].
Step-by-step explanation:
We are given that a random sample of 12 American students had a mean height of 70.2 inches with a standard deviation of 2.73 inches.
A random sample of 18 non-American students had a mean height of 66.9 inches with a standard deviation of 3.13 inches.
Firstly, the Pivotal quantity for 98% confidence interval for the difference between the true means is given by;
P.Q. = ~
where, = sample mean height of American students = 70.2 inches
= sample mean height of non-American students = 66.9 inches
= sample standard deviation of American students = 2.73 inches
= sample standard deviation of non-American students = 3.13 inches
= sample of American students = 12
= sample of non-American students = 18
Also, = = 2.98
<em>Here for constructing 98% confidence interval we have used Two-sample t test statistics.</em>
So, 98% confidence interval for the difference between population means () is ;
P(-2.467 < < 2.467) = 0.98 {As the critical value of t at 28 degree
of freedom are -2.467 & 2.467 with P = 1%}
P(-2.467 < < 2.467) = 0.98
P( < < ) = 0.98
P( < () < ) = 0.98
<u>98% confidence interval for</u> () =
[ , ]
= [ , ]
= [0.56 , 6.04]
Therefore, 98% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students is [0.56 inches , 6.04 inches].