Nora and Oliva separately conduct studies to test H0: = 0.45 against H0: = 0.45, each with n = 485. Nora gets

Nora and Oliva separately conduct studies to test H0: π = 0.45 against H0: π = 0.45, each with n = 485.

Nora gets πˆ = 240/485 = 0.494845 Oliva gets πˆ =

239/485 = 0.492784.

(a) Show that z = 1.99 and P-value = 0.046 for Nora.

Show that z = 1.89 and P-value = 0.058 for Oliva.

(b) Using α = 0.05, indicate in each case whether the result is “statistically significant.” Interpret.

(c) Use this example to explain why important information is lost by reporting the result of a test as “P-value ≤

0.05” versus “P-value > 0.05,” or as “Reject H0” versus

“Do not reject H0,” without reporting the P-value.

(d) The 95% confidence interval for π is (0.451, 0.539)

for Nora and (0.449, 0.537) for Oliva. Explain how this method shows that, in practical terms, the two studies had very similar results.