Question

A well designed and safe workplace can contribute greatly to increased productivity. The accompanying data on maximun weight of lift (MAWL in kg) was randomly selected from the population of healthy males age 18 – 30. Does the following data suggest that the population mean is equal to 25 kg? The population standard deviation is 5.45. Use a significance level of 0.10.

                          25       23       27       21       24       22       23      

	a.	t = 1.44
	b.	z = ± 2.576
	c.	t = 1.943
	d.	Z = - 2.576

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2
	25	2.0409
	23	0.3265
	27	11.7553
	21	6.6121
	24	0.1837
	22	2.4693
	23	0.3265
Total	165	23.7143

Mean X̅ = Σ Xi / n
X̅ = 165 / 7 = 23.5714

To Test :-
H0 :- µ = 25
H1 :- µ ≠ 25

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 23.5714 - 25 ) / ( 5.45 / √( 7 ))
Z = -0.69

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )

Critical value Z(α/2) = Z( 0.01 /2 ) = ± 2.576

| Z | > Z( α/2 ) = 0.6935 < 2.576

Result :- Fail to reject null hypothesis

b.	z = ± 2.576