Question

Assume that z is the test statistic. (Give your answers correct to two decimal places.)

(a) Calculate the value of z for Ho: μ = 10, σ = 2.8, n = 36, x = 11.4.

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(b) Calculate the value of z for Ho: μ = 120, σ = 26, n = 26, x = 125.9.

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(c) Calculate the value of z for Ho: μ = 18.2, σ = 4.4, n = 140, x = 18.88.

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(d) Calculate the value of z for Ho: μ = 81, σ = 13.5, n = 52, x = 78.6.

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Answer 1

Solution:

Given that,

a ) = 10

x = 11.4

σ = 2.8

n = 36

The test statisc z is,

z = (x -  ) /  ( σ /n)

=( 11.4 - 10) / (2.8 / 36 )

= (1.4 *  36 / 2.8 )

= (1.4*36 ) / 2.8

= 3 .00

Test staistic z is = 3.00

b ) = 120

x = 125.9

σ = 26

n = 26

The test statisc z is,

z = (x -  ) /  ( σ /n)

=( 125.9 - 120 ) / (26 / 26 )

= ( 5.9 *  26 / 26 )

= ( 5.9*26 ) / 26

= 1.16

Test staistic z is = 1.16

c ) = 18.2

x = 18.88

σ = 4.4

n = 140

The test statisc z is,

z = (x -  ) /  ( σ /n)

=( 18.88 - 18.2) / (4.4 / 140 )

= (0.68 *  140 / 4.4 )

= (0.68*140 ) / 4.4

= 1.83

Test staistic z is = 1.83

d ) = 81

x = 78.6

σ = 13.5

n = 52

The test statisc z is,

z = (x -  ) /  (  σ /n)

=( 78.6 - 81 ) / (13.5 / 52 )

= ( - 2.4 *  52 / 13.5 )

= ( - 2.4*52 ) / 13.5

= -1.28

Test staistic z is = -1.28