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A variable of a population has a mean of 266and a standard deviation of 16. Ten observations of this variable have a mean of 262I and a sample standard deviation of 20.4Obtain the observed value of the

a. standardized version of x^

b. Studentized version of x¯

Short Answer

Expert verified

Part (a) -0.77

Part (b) -0.60

Step by step solution

01

Part (a) Step 1: Given information

The population mean μ=266and population S.D σ=16

Sample size m=10

Sample mean x¯=262.1

s=20.4

02

Part (a) Step 2: Concept

The formula used: Standardized version of z=x¯-μσn,

03

Part (a) Step 3: Calculation

Standardized version of x¯,z=x¯-μσn

=262.1-2661610=-3.9×1016≈-0.77

As a result, the standardized version of x¯is -0.77

04

Part (b) Step 1: Calculation

Studentized version of x¯,t=x¯-μsn

=262.1-26620.410=-3.9×1020.4≈-0.60

Therefore, the studentized version of x¯ is -0.60

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