Answer :
The test statistic if the sample proportion is 20/50 and the hypothesized proportion was 0.5 is: -1.414.
What is the test statistics?
Using z-test formula to determine the test statistic
z = (p - P) / [tex]\sqrt[/tex]((P(1-P))/n)
Where:
p = sample proportion = 20/50 = 0.4
P = hypothesized proportion = 0.5
n= sample size = 50
Let plug in the formula
Test statistic = (0.4 - 0.5) / [tex]\sqrt[/tex]((0.5(1-0.5))/50)
Test statistic = (-0.1) / [tex]\sqrt[/tex]((0.25)/50)
Test statistic = (-0.1) / [tex]\sqrt[/tex](0.005)
Test statistic = (-0.1) / 0.0707
Test statistic = -1.414
Therefore the test statistic is -1.414.
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