Answer:
The 90% confidence interval
(74.71, 82.63)
Step-by-step explanation:
Confidence Interval Formula is given as:
Confidence Interval = μ ± z (σ/√n)
Where
μ = mean score
z = z score
N = number of the population
σ = standard deviation
The mean is calculated as = The average of their scores
N = 6 students
(71.6 + 81.0 + 88.9 + 80.4 + 78.1 + 72.0 )/ 6
Mean score = 472/6
= 78.666666667
≈ 78.67
We are given a confidence interval of 90% therefore the
z score = 1.645
Standard Deviation for the scores =
s=(x -σ)²/ n - 1 =(71.6 - 78.67)²+(81.0 - 78.67)²+(88.9 - 78.67)² + (80.4 - 78.67)²+ (78.1 - 78.67)²+( 72.0 - 78.67)2/ 6 - 1
= 5.886047531
= 5.89
The confidence interval is calculated as
= μ ± z (σ/√N)
= 78.67 ± 1.645(5.89/√6)
= 78.67 ± 3.9555380987
The 90% confidence interval
is :
78.67 + 3.9555380987 = 82.625538099
78.67 - 3.9555380987 = 74.714619013
Therefore, the confidence interval is approximately between
(74.71, 82.63)
