Jones and Smith separately conduct studies to test H0: = 0.50 against H0: = 0.50,

Jones and Smith separately conduct studies to test H0: π = 0.50 against H0: π = 0.50, each with n =

400. Jones gets πˆ = 220/400 = 0.550.

Smith gets πˆ =

219/400 = 0.5475.

(a) Show that z = 2.00 and P-value = 0.046 for Jones.

Show that z = 1.90 and P-value = 0.057 for Smith.

(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 (0.501, 0.599)

for Jones and (0.499, 0.596) for Smith. Explain how this method shows that, in practical terms, the two studies had very similar results.