Question 974790
This problem is solved using "Sample Distribution of the Proportion"
Use 2-tailed test and the following hypothesis:

Ho:  p1 = p2
H1:  p1 not = p2

p1 = 0.20 and p2 is determined from the binomial distribution since a passenger is either first class or not

p2 = C(n,r) * p1^r * (1-p1)^n-r
p2 = (15! / (5! * (15-5)!)) * (0.20)^5 * (1-0.20)^(15-5)
p2 = ((15*14*13*12*11) / (5*4*3*2*1)) * 0.00032 * 0.107374182
p2 = 3003 * 0.00032 * 0.107374182 = 0.103182294 approx 0.10

p2 is the sample mean and
sample standard deviation is sqrt(pq/n) = sqrt((0.10*0.90)/15) = 0.077459667

now we want to compare p1 and p2 at alpha = 0.10 (using 2-tailed we have 0.05)

t = (0.20 - 0.10) / (0.077459667 / square root(15)) = 5
now t14 for 0.05 is 2.145

Since the test stat is greater than the critical value, we reject the
null at .05 two-tailed significance level