A test of H₀: p = 0.65 against H_a: p < 0.65 based on a sample of size 400 yields the standardized test statistic z = −1.78.

a. Find and interpret the P-value.

b. What conclusion would you make at the α = 0.10 significance level? Would your conclusion change if you used α = 0.05 instead? Explain your reasoning.

c. Determine the value of p̂ = the sample proportion of successes.