Question

`H_0: p = 0.63`
`H_1: p > 0.63`

Your sample consists of 150 subjects, with 96 successes. Calculate the test statistic, rounded to 2 decimal places
`z=`

Answer 1

The test statistic, rounded to 2 decimal places is equal to

How to calculate value of the test statistic?

For this sample, the hypothesis is given by:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

Assuming this sample has a normal distribution, we would use a pooled z-test to determine the value of the test statistic:

Substituting the given parameters into the formula, we have;

$z = \frac{\frac{96}{150} \;-\;0.63}{\sqrt{0.63\; +\; \frac{1\;-\;0.63}{150}} }\\\\z = \frac{0.64 \;-\;0.63}{\sqrt{0.63\; +\; \frac{0.37}{150}}}\\\\z = \frac{0.01}{\sqrt{0.63\; +\; 0.0025}}\\\\z = \frac{0.01}{\sqrt{0.6325}}$

z = 0.01/0.7953

z = 0.013.

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