Question
In: Statistics and Probability
How does the length of the 95% t confidence interval compare with that of the 95%...
How does the length of the 95% t confidence interval compare with that of the 95% z confidence interval? Very confused on this
Solutions
Expert Solution
The length of the 95% t confidence interval is always greater than or equal to the 95% z confidence interval.
If the sample size is very small, then the length of the 95% t confidence interval will be greater than the 95% z confidence interval.
As we increase sample size, the length of the 95% t confidence interval will be decrease.
For very large sample size, the length of the 95% t confidence interval and 95% z confidence interval will be approximately same.
For example, for sample size n = 10,000, both confidence intervals will be same. There length of the both confidence intervals will be same.
But, for sample size of n = 10, there will be bigger difference in the both intervals.
orchestra answered 2 years agoRelated Solutions
What does a 95% confidence interval mean?
What does a 95% confidence interval mean?
The length of a 95% confidence interval for mean Children is which of the following? (Because...
The length of a 95% confidence interval for mean Children is
which of the following? (Because of potential roundoff, choose the
closest.)
a.0.341
b. 0.369
c. 0.407
d. 0.467
Person
Gender
Married
Age
Children
Salary
Spent
1
Male
No
28
1
48600
750
2
Male
Yes
35
2
75500
1980
3
Female
No
33
2
58900
1820
4
Female
Yes
53
1
92200
990
5
Female
No
49
1
100700
1990
6
Male
Yes
57
1
128900
1900
7
Female...
The length of a 95% confidence interval for mean Children is which of the following? (Because...
The length of a 95% confidence interval for mean Children is
which of the following? (Because of potential roundoff, choose the
closest.)
data:
Person
Gender
Married
Age
Children
Salary
Spent
1
Male
No
28
1
48600
750
2
Male
Yes
35
2
75500
1980
3
Female
No
33
2
58900
1820
4
Female
Yes
53
1
92200
990
5
Female
No
49
1
100700
1990
6
Male
Yes
57
1
128900
1900
7
Female
Yes
53
1
84900
1000
8...
The length of a 95% confidence interval for mean Children is which of the following? (Because...
The length of a 95% confidence interval for mean Children is
which of the following? (Because of potential roundoff, choose the
closest.)
Person
Gender
Married
Age
Children
Salary
Spent
1
Male
Yes
35
1
78900
1610
2
Male
Yes
53
1
114100
1960
3
Male
Yes
36
2
84800
1470
4
Female
Yes
51
2
87500
1210
5
Male
Yes
39
2
85600
1320
6
Male
Yes
66
3
112800
310
7
Male
Yes
48
1
87300
1070
8
Male...
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23 45 43 34 26 36 67 45 43 55 53 42 87 65 45 51 53 54 54 48 49
54 53 52 54
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waiting time before seeing a medical professional was 14 minutes
and the standard deviation was 9 minutes. Assume the waiting times
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construct the...
Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the...
Use the standard normal distribution or the t-distribution to
construct a 95% confidence interval for the population mean.
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b) a 90%confidence interval based on df=9
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Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the...
Use the standard normal distribution or the t-distribution to
construct a 95% confidence interval for the population mean.
Justify your decision. If neither distribution can be used,
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