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What is the test statistic if the sample proportion is [tex]\frac{20}{50}[/tex] and the hypothesized proportion is [tex]0.5[/tex]?

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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