In this scenario, we are dealing with population proportion. The formula for calculating the test statistic for a population proportion is expressed as
test statistic = (sample proportion - claimed proportion)/standard error
From the information given,
claimed proportion, p = 0.72
q = 1 - p = 1 - 0.72 = 0.28
number of samples, n = 51
number of success from the sample, x = 37
Sampe proportion, p' = x/n = 37/51 = 0.7255
In this case, the formula for calculating standard error is expressed as
[tex]\begin{gathered} \text{standard error = }\sqrt[]{\frac{pq}{n}}\text{ = }\sqrt[]{\frac{0.72\text{ }\times0.28}{51}} \\ \text{standard error = 0.06287} \end{gathered}[/tex]
Thus,
Test statistic, z = (0.7255 - 0.72)/0.06287
z = 0.087
