In: Statistics and Probability
Data for 64 female college athletes was collected. The data on weight (in pounds) are roughly bell shaped with x overbar equals 132x=132 and s equals 13s=13. Complete parts a and b below.
a. Give an interval within which about 68% of the weights fall.
Solution :
Given that,
Point estimate = sample mean =
= 132
sample standard deviation = s = 13
sample size = n = 64
Degrees of freedom = df = n - 1 = 63
At 68% confidence level the t is ,
= 1 - 68% = 1 - 0.68 = 0.32
/ 2 = 0.32 / 2 = 0.16
t
/2,df = t0.16,63 = 1.002
Margin of error = E = t/2,df
* (s /
n)
= 1.002 * (13 /
64)
= 1.628
The 68% confidence interval is,
- E <
<
+ E
132 - 1.628 <
< 132 + 1.628
130.312 <
< 133.628
(130.312 , 133.628)