Question

For all problems below, use correct notation where appropriate.
Round all proportions to 3 d.p. and standard errors to 4 d.p.
1. Do we dream in color? In the 1940s, before the age of television, color movies, and video games, 29% of the American population reported dreaming in color. A psychologist suspects that the present-day proportion might be higher, now that we are surrounded with color imagery. In a random sample of 113 people, 92 reported dreaming in color (Schwitzgebel 2003).
a) State the parameter to be tested. Be specific.
b) Conduct a hypothesis test to determine if the psychologist’s suspicion is correct. Clearly, show all 7 steps as shown in the lecture notes. Complete each
step by hand. Be sure to state the hypotheses in words and symbols.
c) In the context of this problem, what would it mean if we made a Type I error? What is the probability of making this kind of error?

Answer 1

a)
parameter: population proportion

b)
H0: p = 0.29
Ha: p > 0.29

pcap = 92/113 = 0.814

SE = sqrt(0.29 * 0.71/113) = 0.0427

Test statistic,
z = (pcap - p)/SE
z = (0.814 - 0.29)/0.0427
z = 12.27

p-value = 0.0000

Here significance level is 0.05
this is right tailed test, hence rejection region lies to the right of the curve.

Reject H0: if z > 1.64

Reject H0
There are significant evidence to conclude that the proportion is higher than 0.29.

c)
type I error occurs when one incorrectly rejects the null hypothesis
Here, we concluded that the proportion is higher than 0.29 however in reality it is not.

Probability = significance level = 0.05