In: Statistics and Probability
show your work please
In a study of speed dating conducted at Columbia University, 15 female subjects were asked to rate the attractiveness of their male dates, and a sample showed the results to be a mean of 7.35 and standard deviation of 2.70. Construct a 95% confidence interval.
final answer
Lower | |
Upper |
Solution :
Given that,
= 7.35
s =2.71
n = 15
Degrees of freedom = df = n - 1 = 15- 1 = 14
a ) At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2= 0.05 / 2 = 0.025
t /2,df = t0.025,14 = 2.145 ( using student t table)
Margin of error = E = t/2,df * (s /n)
= 2.145* ( 2.70/ 15)
= 1.4954
The 95% confidence interval estimate of the population mean is,
- E < < + E
7.35 - 1.4954 < <7.35 + 1.4954
5.8546 < < 8.8454
( lower limit=5.8546 ,upper limit= 8.8454)