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. (up to 5 EC pts) 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 and use the appropriate notation.
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? (See 8.1,8.2 lecture notes.)

Answer 1

sample size =n=113

number of peoples dreaming in color=x=92

so sample proportion is given by

a)

we are testing the proportion of peoples dreaming in color so the Proportion of peoples dreaming in color is the parameter of interest

b)

we are interested in testing that if the proportion is increased from 0.29 or not hence

H0:P=0.29 H1:P>0.29

now test statistics is given by

So P-Value =P(Z>12.2756) =0

Hence here P-Value is less than any possible level of significance hence we reject H0 that is there is sufficient evidence to conclude that proportion is more than 0.29

c)

Type 1 error is defined as rejecting H0 while in actual H0 is true so in our case we have concluded that proportion is more than 0.29 while in actual proportion is 0.29

P(type 1 error) =level of significance =0.05