Question

Import the "reacttimes" 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.

Answer 1

This question is incomplete, here is the complete question:

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 )