Answer:
3.573 to 4.127
Step-by-step explanation:
Given
Sample size = 15
Mean = Sum of ratings/ sample size
Mean = 57.7/15
Mean = 3.85
Degree of freedom = sample size - 1
Degree of freedom = 15 - 1 = 14
df = 14
Then we calculate the standard deviation
(x - mean)² ||
(3.6 - 3.85)² || 0.0625
(2.9 - 3.85)² || 0.9025
(3.8 - 3.85)² || 0.0025
(4.5 - 3.85)² || 0.4225
(3.2 - 3.85)² || 0.4225
( 3.9 - 3.85)² || 0.0025
( 3.3 - 3.85)² || 0.3025
( 4.6 - 3.85)² || 0.5625
(4.1 - 3.85)² || 0.0625
(4.3 - 3.85)² || 0.2025
4.4 - 3.85)² || 0.3025
( 3.9 - 3.85)² || 0.0025
(3.2 - 3.85)² || 0.4225
( 4.2 - 3.85)² || 0.1225
( 3.8 - 3.85)² || 0.0025
Total || 3.7975
Variance = 3.7975/15 = 0.253167
Standard Deviation = √0.253167 = 0.50315703314174194
Standard Deviation = 0.5 ------- Approximated
The next step is to subtract the confidence level from 1, then divide by two.
i.e (1 - 0.95)/2 = 0.025
α = 0.025
Then we look up this answer to step in the t-distribution table.
For 14 degrees of freedom (df) and α = 0.025, my result is 2.145
The next step is to divide the sample standard deviation by the square root of the sample size.
0.5 / √15 = 0.129
Next is to multiply this result by step 2.145 (from the t table)
0.129 × 2.45 = 0.277
For the lower end of the range, subtract 0.277 from the sample mean.
3.85 – 0.277 = 3.573
Step 7: For the upper end of the range, add step 0.277 to the sample mean.
3.85 + 0.277 = 4.127
