Import the "reacttimes" data set and consider the 50 observations of the variable "Times" to be a sample from a larger populatio
n. Find a 99% confidence interval for the population mean. Construct a normal quantile plot and comment on the appropriateness of the procedure.
1 answer:
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Import the "react times" data set and consider the 50 observations of the variable "Times" to be a sample from a larger population. Find a 99% confidence interval for the population mean. Construct a normal quantile plot and comment on the appropriateness of the procedure.
Times
0.12
, 0.3
, 0.35
, 0.37
, 0.44
, 0.57
, 0.61
, 0.62
, 0.71
, 0.8
, 0.88
, 1.02
, 1.08
, 1.12
, 1.13
, 1.17
, 1.21
, 1.23
, 1.35
, 1.41
, 1.42
, 1.42
, 1.46
, 1.5
, 1.52
, 1.54
, 1.6
, 1.61
, 1.68
, 1.72
, 1.86
, 1.9
, 1.91
, 2.07
, 2.09
, 2.16
, 2.17
, 2.2
, 2.29
, 2.32
, 2.39
, 2.47
, 2.6
, 2.86
, 3.43
, 3.43
, 3.77
, 3.97
, 4.54
, 4.73
Answer: confidence interval = ( 1.3524, 2.1323
Explanation:
so we have 50 observations/ react times hence we use z-test for the mean
SUM OF OBSERVATION (∑x) = 87.12
SUM OF SQUARE = (∑x²) = 207.9336
100 ( 1 - ∝ ) % confidence interval for population mean is
mean = 87.12 / 50 = 1.7429
S² = I/49 ( 207.9336 - 50(1.7429)²)
S² = 1.145627
S = √1.145627 = 1.07034
FOR ∝ = 0.01
Z₍ ₀.₀₁/₂₎ = 2.57583
so confidence interval = ( 1.7429 - 2.57583 × 1.07039/√50, 1.7429 + 2.57583 × 1.07039/√50)
confidence interval = ( 1.3524, 2.1323 )
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