Step 1 :State the null hypothesis (H0) and the alternative hypothesis (H1). H0: P = 0.56, H1: P ≠ 0.56
Step 2 :Calculate the sample proportion (p̂) by dividing the number of successful outcomes by the sample size. In this case, p̂ = 280 / 750 = 0.3733
Step 3 :Calculate the test statistic (z0) using the formula: z0 = (p̂ - P0) / sqrt[(P0(1 - P0)) / n]. Here, P0 is the proportion in the null hypothesis and n is the sample size
Step 4 :Substitute the values into the formula: z0 = (0.3733 - 0.56) / sqrt[(0.56(1 - 0.56)) / 750]
Step 5 :Simplify the expression inside the square root: z0 = -0.1867 / sqrt[0.2464 / 750]
Step 6 :Calculate the denominator: z0 = -0.1867 / 0.0181
Step 7 :Finally, calculate the test statistic: z0 = -10.32
Step 8 :So, the test statistic z0 is approximately \(\boxed{-10.32}\) (rounded to two decimal places)