Answer:
Explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for people over the age of 55 and people under the age of 25. The population proportion of people over the age of 55 and people under the age of 25 who dream in black and white would be p1 and p2 respectively.
p1 - p2 = difference in the proportion of people over the age of 55 and people under the age of 25 who dream in black and white.
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
H1 : p1 > p2
p1 - p2 > 0
it is a right tailed test
Sample proportion = x/n
Where
x represents number of success(number of complaints)
n represents number of samples
For people over the age of 55,
x1 = 76
n1 = 301
p1 = 76/301 = 0.25
For people under the age of 25,
x2 = 10
n2 = 311
p2 = 10/311 = 0.032
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (76 + 10)/(301 + 311) = 0.14
1 - pc = 1 - 0.14 = 0.86
z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.25 - 0.032)/√(0.14)(0.86)(1/301 + 1/311) = 0.218/0.02805598439
z = 7.71
From the normal distribution table, the p value is
p < 0.00001
Since 0.01 > 0.00001, we would reject the null hypothesis.
Therefore, the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25.