Question

Hi, can you help me answer this question please, thank you

Answer 1

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

`\begin{gathered} \text{standard error = }\sqrt[]{(pq)/(n)}\text{ = }\sqrt[]{\frac{0.72\text{ }*0.28}{51}} \\ \text{standard error = 0.06287} \end{gathered}`

Thus,

Test statistic, z = (0.7255 - 0.72)/0.06287

z = 0.087