Mark Biagi
Homework #7
Activity 168
A.
The number of essays required for a confidence interval of 99% is .01=2.576(square root of
(.15)(.85)/n.
Solving for the equation n = 8461.
B.
Two ways to accomplish this would be to use a lower confidence interval of say 90%. You
could also use a wider margin of error of .03.
Activity 1612
A.
The margin of error is 100%95%=5%/2=2.5%.
B.
The confidence interval is (74.87, 77.13).
This interval means that 95% of samples will have
a mean between 74.87% and 77.13%.
C.
The study did use a random sample size which satisfies the first rule.
Since n pos greater
than 10 and n(1P) is also greater than 10, the technical conditions are satisfied.
Activity 1614
A.
A 95% confidence interval for the proportion is .54 plus or minus (1.96) x square root of .
54(.66)/1208 = .5554 plus or minus (1.96)(0.1434) = .54 plus or minus 0.281 = (.512, .568).
B. Yes, since all of the numbers in the interval are bigger than 50 it suggests that more than half
of viewers supported Santos.
Activity 1617
A.
The proportion of simulated repetitions that resulted in no mother getting the
correct baby was 358/1000 = .358.
B.
For a 95% CI, you calculate .358 plus or minus 1.96 times the square root of .
358(1.642)/1000= .358 plus or minus (1.96)(.015) 
(.355, .361).
C.
You are 95% confident the longterm proportion of times that no mother would
get the correct baby is between .355 and .361.
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D. π = 3.75
E.
Yes, the 95% confidence interval succeeds in capturing the population parameter.
F.
If 1000 different statistics classes carried out this simulation, you would expect roughly 95%
or 950 of their intervals to succeed in capturing π = .375, whereas you would expect about 50 of
these intervals not to contain .375.
G.
For an 80% CI, you calculate, .359 plus or minus
(1.282)(.01517) = .359 plus or minus
.
0194 = (.34, .38).
Yes, this interval just succeeds in capturing
π
=.375.
If 1000 different statistics classes carried out this simulation, you would expect roughly 80% or
800 of their intervals to succeed in capturing π
=
.375, whereas you would expect about 200 of
these intervals not to contain .375.
Activity 176
A
.
You would reject the null hypothesis at the
a =
.10 level because the
p
value is less than .05
and therefore less than .10.
B
.
You do not have enough information to know whether you would reject the null hypothesis at
the a
= .01 level. Although you know the
p
value is less than .05, you do not know whether it is
less than .01.
C
.
You know that you would fail to reject the null hypothesis at the
a =
.03 level because you
know the
p
value is greater than .05 and therefore greater than .03.
D
.
You do not have enough information to know whether you would reject the null hypothesis at
the a = .07 level. Although you know the
p
value is greater than .05, you do not know whether it
is greater than .07.
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 Spring '10
 Garant
 Null hypothesis, Statistical hypothesis testing

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