Question
In: Statistics and Probability
Using a t-distribution table or software or a calculator, report the t-statistic which is multiplied by...
Using a t-distribution table or software or a calculator, report the t-statistic which is multiplied by the standard error to form the margin of error for the following cases.
a. 90% confidence interval for a mean with 16 observations.
b. 90% confidence interval for a mean with 26 observations.
c. 98% confidence interval for a mean with 26 observations.
a. t = _____ (round to three decimal places)
b. t = _____ (round to three decimal places)
c. t = _____ (round to three decimal places)
Solutions
Expert Solution
Solution :
Given that,
a) sample size = n = 16
Degrees of freedom = df = n - 1 = 16 - 1 = 15
At 90% confidence level
= 1 - 90%
=1 - 0.90 =0.10
/2
= 0.05
t/2,df
= t0.05,15 = 1.753
b) sample size = n = 26
Degrees of freedom = df = n - 1 = 26 - 1 = 25
At 90% confidence level
= 1 - 90%
=1 - 0.90 =0.10
/2
= 0.05
t/2,df
= t0.05,25 = 1.708
c) sample size = n = 26
Degrees of freedom = df = n - 1 = 26 - 1 = 25
At 98% confidence level
= 1 - 98%
=1 - 0.98 =0.02
/2
= 0.01
t/2,df
= t0.01,25 = 2.485
orchestra answered 2 years agoRelated Solutions
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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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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...
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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...
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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
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values for the Student's t distribution. Use an
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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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