A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 301 people over the age of 55, 76 dream in black and white, and among 311 people under the age of 25, 10 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below.

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.