Question

1.

H 0 : p = 0.73

H 1 : p ≠ 0.73

Your sample consists of 83 subjects, with 59 successes. Calculate the test statistic, rounded to 2 decimal places z =_________________

2.  

Testing:

H0:μ=27.5
H1:μ<27.5

Your sample consists of 22 subjects, with a mean of 26.1 and standard deviation of 4.55.

Calculate the test statistic, rounded to 2 decimal places.

t=__________

Answer 1

1. Solution :

Given that H 0 : p = 0.73

H 1 : p ≠ 0.73

=> from given information ,

=> x = 59 , n = 83

=> p^ = x/n

= 59/83

= 0.7108

= 0.71 (rounded)

=> q = 1 - p = 0.27

=> Test statistic Z = (p^ - p)/sqrt(p*q/n)

= (0.71 - 0.73)/sqrt(0.73*0.27/83)

= -0.4104

= -0.41 (rounded)

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2. Solution :

Given that mean x-bar = 26.1 , standard deviation s = 4.55 , n = 22 , μ = 27.5

=> Test statistic t = (x-bar - μ)/(s/sqrt(n))

= (26.1 - 27.5)/(4.55/sqrt(22))

= -1.4432

= -1.44 (rounded)