Question

16 students were randomly selected from a large group of students taking a certain calculus test. The mean score for the students in the sample was 86 and the standard deviation was 1.3. Assume that the scores are normally distributed. Construct a 98% confidence interval for the mean score, μ, of all students taking the test. Round your answer to two decimal places.

Answer 1

Solution :

Given that,

= 86

s =1.3

n =16

Degrees of freedom = df = n - 1 =16 - 1 =15

a ) At 98% confidence level the t is

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

t /2,df = t0.01,15 =2.602 ( using student t table)

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

=2.602 * (1.3 / 16)

= 0.85

The 98% confidence interval estimate of the population mean is,

- E < < + E

86- 0.85 < < 86+ 0.85

85.15 < < 86.85

(85.15, 86.85 )