The sampling distribution has a mean of 0.03 and a standard error of 0.007. The researchers' sample mean comes back at 0.026. In other words, only 2.6% of the children on the drug experienced food allergies in their youth. What is the z-score for this sample mean?

z = - 0.57

Step-by-step explanation:

A z-score indicates how much away is something from the mean so it can be more (above) than the mean or less (below) than the mean.

sampling distribution mean = 0.03

standard error = 0.007

researcher's sample mean = 0.026

z = (0.026 - 0.03) / 0.007

z = (-0.004) / 0.007

z = - 0.57

So that means the researcher's sample mean is 0.57 standard deviation below the sampling distribution mean.

The negative sign above is the indicator of below the mean value.