Consider the following sets of replicate measurements:( 2.6, 2.7, 2.8, 3.0, 3.2) Calculate the 95% confidence interval .
*
2 points
non of all
2.68 ± 0.30
2.86 ± 0.40
2.86 ± 0.030
To calculate the 95% confidence interval of the set of measurements (2.6, 2.7, 2.8, 3.0, 3.2), we first need to calculate the mean and standard deviation of the measurements.
Mean:
(2.6 + 2.7 + 2.8 + 3.0 + 3.2) / 5 = 2.86
Standard Deviation:
s = √ [(Σ (x - x̄)^2) / (n - 1)]
= √ [((2.6 - 2.86)^2 + (2.7 - 2.86)^2 + (2.8 - 2.86)^2 + (3.0 - 2.86)^2 + (3.2 - 2.86)^2) / 4]
= √ [((-0.26)^2 + (-0.16)^2 + (-0.06)^2 + (0.14)^2 + (0.34)^2) / 4]
= √ [(0.0676 + 0.0256 + 0.0036 + 0.0196 + 0.1156) / 4]
= √ [0.2312 / 4]
= √ 0.0578
≈ 0.24
95% Confidence Interval:
n = 5
Degrees of freedom (df) = n - 1 = 4
T value for 95% confidence with 4 degrees of freedom = 2.776
Margin of error = T * (s / √n)
= 2.776 * (0.24 / √5)
≈ 0.22
95% Confidence Interval:
Lower bound = mean - margin of error
= 2.86 - 0.22
= 2.64
Upper bound = mean + margin of error
= 2.86 + 0.22
= 3.08
Therefore, the 95% confidence interval for the set of replicate measurements is approximately 2.64 to 3.08. However, this option is not given in the choices provided, so the closest option is "2.68 ± 0.30".