Question
In: Math
Method 1: Use the Student's t distribution with d.f. = n − 1. This is the...
Method 1: Use the Student's t distribution with
d.f. = n − 1.
This is the method used in the text. It is widely employed in
statistical studies. Also, most statistical software packages use
this method.
Method 2: When n ≥ 30, use the sample standard
deviation s as an estimate for σ, and then use
the standard normal distribution.
This method is based on the fact that for large samples, s
is a fairly good approximation for σ. Also, for large
n, the critical values for the Student's t
distribution approach those of the standard normal
distribution.
(d) Now consider a sample size of 71. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.
| 90% | 95% | 99% | |
| lower limit | |||
| upper limit |
(e) Compute 90%, 95%, and 99% confidence intervals for μ
using Method 2 with the standard normal distribution. Use
s as an estimate for σ. Round endpoints to two
digits after the decimal.
| 90% | 95% | 99% | |
| lower limit | |||
| upper limit |
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milcah answered 4 months agoRelated Solutions
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical values for the
Student's t distribution. Use an appropriate d.f. as the row
header. For a right-tailed test, the column header is the value of
α found in the one-tail area row. For a left-tailed test, the
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13) The Student's t distribution table gives critical values for the Student's t distribution. Use an...
13)
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value...
12) The Student's t distribution table gives critical values for the Student's t distribution. Use an...
12)
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
αfound in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value of...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value...
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What happens to a Student's t-distribution as the degrees of
freedom increase?
a.A student's t-distribution diverges from the standard normal
distribution as the degrees of freedom increases
b.A student's t-distribution converges to the standard normal
distribution as the degrees of freedom increases
a) Use the Student's t-distribution to find the t-value for each of the given scenarios. Round...
a) Use the Student's t-distribution to find the t-value for each
of the given scenarios. Round t-values to four decimal places.
Find the value of t such that the area in the right tail of the
t-distribution is 0.01, if the sample size is 89.
t=
Find the value of t such that the area in the left tail of the
t-distribution is 0.0005, if the sample size is 134.
t=
Find the value of t such that the area...
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