Question

In previous generations it was believed that people dreamed in black and white rather than colour. A recent hypothesis is that North Americans did dream in black and white in the era of the black-and-white television, but that North Americans now dream in colour after the introduction of colour television and other media. To test this, researchers performed a survey based research with 30 older individuals (from the black and white era) and 30 younger individuals (from the colour era). For the two groups, the researchers determined the percentage of colour dreams that each individual experienced.
Older group (black and white era): Ȳ= 33.9%, s = 36.9%
Younger group (colour era): Ȳ= 68.4%, s = 31.8%
a. What test would you use to determine if technology influences whether people dream in black and white or colour? Justify your answer.
b. State a HO and HA.
c. What is the sample variance for each group?
d. How many degrees of freedom are associated with each group?
e. Calculate the pooled variance for these data.
f. What is the standard error of the difference between means?
g. Calculate t for this test.
h. How many degrees of freedom will this test have?
i. What is the critical value for the test corresponding to α = 0.05? What is the critical value for the test corresponding to α = 0.01?
j. What is the P-value associated with the test statistic?

*******How to find P-value here?*******

Answer 1

Answer:

a):
t test for difference of means with population variances are equal if technology influences
whether people dream in black and white or colour .
b):
null, Ho: u1 = u2
alternate, H1: u1 != u2
c):
sample variance of older group = 1361.61%
sample variance of younger group= 1011.24%
d):
degree of freedom of older group
the value of |t α| with n-1 = 29 d.f is 2.756
degree of freedom of younger group
the value of |t α| with n-1 = 29 d.f is 2.756
e):
pooled variance s^2 = 1186.425
f):
standard error = sqrt(S^2(1/n1+1/n2))
=sqrt( 1186.425 * (1/30+1/30) )
=8.894
g):
test statistic: -3.8792
h):
critical value: -2.66 , 2.66
i):
level of significance=0.05
critical value
the value of |t α| with (n1+n2-2) i.e 58 d.f is 2
level of significance=0.01
critical value
the value of |t α| with (n1+n2-2) i.e 58 d.f is 2.66
decision: reject Ho
j ):
test statistic: -3.8792

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