Question

The authors of the article Boredom in Young adults–Gender and Cultural Comparisons administered the Boredom Proneness Scale to 97 male U. S. college students and found a sample mean of x = 10.40 with a sample standard deviation of s = 4.83. Calculate a 95% confidence interval for the true mean boredom proneness of male college students.

Answer 1

Solution :

Given that,

= 10.40

s =4.83

n =97

Degrees of freedom = df = n - 1 =97 - 1 = 96

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,96 =  1.985 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 1.985* ( 4.83/ 97)

E = 0.9735

The 95% confidence interval estimate of the population mean is,

- E < < + E

10.40- 0.9735< <10.40 + 0.9735

9.4265 < < 11.3735

(9.4265 , 11.3735 )