Question

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 290 people over the age of​ 55, 71 dream in black and​ white, and among 296 people under the age of​ 25, 10 dream in black and white. Use a 0.050 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.

Identify the test statistic?

Identify the p value?

Test the claim by constructing an appropriate confidence level?

What is the conclusion base on the hypothesis test?

What is the conclusion base on the confidence level?

Answer 1

The null and alternate hypothesis are:

H0:

Ha:

The test statistic value is given by:

The p-value is less than 0.00001.

Since the p-value is less than the level of significance 0.05, so we have sufficient evidence to reject H0.

Thus we say that i.e. the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25.