Statistik, hypotestest

Hej! Jag håller på att plugga till en omtenta i statistik och har löst nedan uppgift, finns inget facit på denna så hade behövt hjälp att kolla om jag tänkt/räknat rätt? (pluggar i USA därmed engelska)

Frågan lyder: 

"A startup company is about to Market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40 percent of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contact 420 randomly chosen adults and finds that 181 of them know that this company manufactures printers. Would you recommend the company to continue to advertise during Super Bowl? Explain."

a) State null hypothesis         = (p ≤ 0.40)

b) state non null hypothesis = (p > 0.40)

c) state standard deviation = σ = sqrt[(p̂ * (1 - p̂)) / n] σ = sqrt[(0.431 * (1 - 0.431)) / 420] ≈ 0.0256

d) state test statistic =  z = (0.431 - 0.40) / 0.0256 ≈ 1.2109

e) state p value  = P(Z > 1.2109) ≈ 0.1136

 

Then solve following quesions about 95% confidence interval:

 

f) state SE = SE = sqrt[(0.431 * (1 - 0.431)) / 420] ≈ 0.0256

g) state critical value = 1.645?

h) state confidence interval lower limit  = Lower limit = p̂ - (critical value * SE) Lower limit = 0.431 - (1.645 * 0.0256) ≈ 0.391

i) state confidence interval higher value = Upper limit = p̂ + (critical value * SE) Upper limit = 0.431 + (1.645 * 0.0256) ≈ 0.471