Test Statistic

Question

You are going to test the claim that less than 60% of women do the income

taxes for their household.

In a random sample of 600 women, 345 of them do the income taxes

for their household.

Calculate the test statistic.

Round your answer to two decimal places.

Answer 1

Test statistic = (p* - p) / σ_P

 

Where σ_P = √(p)(q)/n,

 

p* = x / n (sample proportion)

p = 0.600 (population proportion parameter)

 

q = 1 - p 

n = sample size (# of women)

x = successes (# of women who do income taxes for household)

 

p*

= x / n

= 345/600

= 0.575

 

p = 0.600

 

q

= 1 - p

= 1 - 0.600

= 0.400

 

σ_P

= √(p)(q)/n

= √(0.600)(0.400)/600

= 0.020

 

Test statistic

= (0.575 - 0.600)/0.020

= -1.25

Answer 2

345/600 = 0.575 or 57.5% and that is indeed < 60%