Question

The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution.

Test H₀ : p₁ = p₂ vs Hₐ : p₁

from the randomization distribution is 0.06 Find the value of the standardized z-test statistic.

Answer 1

To calculate the z-test statistic, use the formula (X - μX) / σX, substituting 16 for X, 16.43 for μX, and 0.06 for σX to get a z value of approximately -7.17.

Step-by-step explanation:

To find the value of the standardized z-test statistic given a set of hypotheses and the standard error from a randomization distribution, one typically uses the formula:

z = (X - μX) / σX

Where:

X is the sample mean,

μX (mu) is the population mean under the null hypothesis,

σX (sigma) is the standard error of the sample mean.

In this case, we have:

The sample mean (X) = 16,

The population mean under the null hypothesis (μX) = 16.43,

The standard error (σX) = 0.06 (as given by the randomization distribution).

The z-test statistic is then calculated as:

z = (16 - 16.43) / 0.06

Plug in the values to obtain:

z ≈ -7.17

This is the z-test statistic that can be compared to critical values to make a decision about the null hypothesis.