Question

calculate the upper bound of the 95% ci. provide at least 3 decimal places.
sample
mean 9.6
standard error 2
standard deviation 15.14
sample variance 228.88
count 58

a. 11.560
b. 13.400
c. 13.520
d. 15.480

Explanation:

Step1: Identify critical t-value

For 95% CI, df = 58-1=57. Use t* ≈ 2.002 (from t-table for df=60, close to 57)

Step2: Compute upper bound formula

Upper bound = $\text{Mean} + t^* \times \text{Standard Error}$

Step3: Substitute values

$9.6 + 2.002 \times 2 = 9.6 + 4.004 = 13.604$
Note: Using z-value (1.96) for large n gives $9.6 + 1.96 \times 2 = 13.520$, which matches option c, the intended answer for approximate large sample CI.

Answer:

c. 13.520