41.
A poll showed that
5757%
of randomly surveyed adults in a certain country said their country benefits from having a rich class. Complete parts (a) through (h) below.a. Assuming the sample size was
400400,
how many would have said that their country benefits from having a rich class?Assuming the sample size was
400400,
nothing
people in the sample would have said that their country benefits from having a rich class.
(Round to the nearest integer as needed.)
b. Is the sample size large enough to apply the Central Limit Theorem? Explain. Assume the other conditions for using the CLT are met.
Select the correct choice below and fill in the answer box(es) to complete your choice.
(Round to the nearest integer as needed.)
A.Yes, the sample size is large enough, since the expected number of successes is
nothing
and the expected number of failures is
nothing,
both of which are greater than or equal to 10.
B.Yes, the sample size is large enough, since the estimated standard error is
nothing,
which is greater than or equal to 10.
C.No, the sample size is not large enough, since the expected number of successes is
nothing
and the expected number of failures is
nothing,
at least one of which is less than 10.
D.No, the sample size is not large enough, since the estimated standard error is
nothing,
which is less than 10.
c. Find a 95% confidence interval for the percent that believe that their country benefits from having a rich class, using the numbers from part (a).
The 95% confidence interval is
left parenthesis nothing % comma nothing % right parenthesis%,%.
(Round to one decimal place as needed.)
d. Find the width of the interval you found in part (c) by subtracting the lower boundary from the upper boundary.
The width of the interval is
nothing%.
(Round to one decimal place as needed.)
e. Now assuming the sample size was multiplied by
99
(nequals=36003600)
and the percentage was still
5757%,
how many would have said their country benefits from having a rich class?Assuming the sample size was
36003600,
nothing
would have said they were thriving.
(Round to the nearest integer as needed.)
f. Find a 95% confidence interval, using the numbers from part (e).
The 95% confidence interval is
left parenthesis nothing % comma nothing % right parenthesis%,%.
(Round to one decimal place as needed.)
g. What is the width of the interval you found in part (f)?
The width of the interval is
nothing%.
(Round to one decimal place as needed.)
h. When the sample size is multiplied by
99
is the width of the interval divided by
99?
If not, what is it divided by? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.No, when the sample size is multiplied by
99,
the width of the interval is divided by
nothing.
(Round to the nearest integer as needed.)
B.Yes, when the sample size is multiplied by
99,
the width of the interval is divided by
99.
Click to select your answer(s).
a) np = 400*0.57 = 228
b)
A.Yes, the sample size is large enough, since the expected number of successes is 228
and the expected number of failures is (400-228) = 172
both of which are greater than or equal to 10.
c)
Level of Significance, α =
0.05
Number of Items of Interest, x =
228
Sample Size, n = 400
Sample Proportion , p̂ = x/n =
0.5700
z -value = Zα/2 = 1.960 [excel
formula =NORMSINV(α/2)]
Standard Error , SE = √[p̂(1-p̂)/n] =
0.0248
margin of error , E = Z*SE = 1.960
* 0.0248 = 0.0485
95% Confidence Interval is
Interval Lower Limit = p̂ - E = 0.570
- 0.0485 = 0.5215
Interval Upper Limit = p̂ + E = 0.570
+ 0.0485 = 0.6185
95% confidence interval is ( 52.1% < p <
61.9% )
d)The width of the interval is 9.7%
e) np=3600*0.57=2052
f)
Level of Significance, α =
0.05
Sample Size, n = 3600
Sample Proportion , p̂ = x/n =
0.5700
z -value = Zα/2 = 1.960 [excel
formula =NORMSINV(α/2)]
Standard Error , SE = √[p̂(1-p̂)/n] =
0.0083
margin of error , E = Z*SE = 1.960
* 0.0083 = 0.0162
95% Confidence Interval is
Interval Lower Limit = p̂ - E = 0.570
- 0.0162 = 0.554
Interval Upper Limit = p̂ + E = 0.570
+ 0.0162 = 0.586
95% confidence interval is ( 55.4% < p <
58.6% )
g) width = 3.2%
h) A.No, when the sample size is multiplied by 9 ,the width of the interval is divided by 3
41. A poll showed that 5757% of randomly surveyed adults in a certain country said their...
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