In: Statistics and Probability
Suppose you are running the bowling alley and are interested in finding the distribution of shoe sizes for women in order to buy a good fitting distribution of shoes. You took a random sample of 36 women and the mean size was an 8 with a standard deviation of 2. Create and interpret an approximate 95% confidence interval, with the appropriate critical T or Z value, for the mean shoe size of all women.
Solution :
Given that,
= 8
s = 2
n = 36
Degrees of freedom = df = n - 1 = 36 - 1 = 35
At 95% confidence level the t is ,
=
1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
t
/2,df = t0.025,35 =2.030
Critical t value = 2.030
Margin of error = E = t/2,df
* (s /
n)
= 2.030 * ( 2 /
36)
= 0.68
Margin of error = 0.68
The 95% confidence interval estimate of the population mean is,
- E <
<
+ E
8 - 0.68 <
< 8 + 0.68
7.32 <
< 8.68
(7.32 , 8.68)