We use the t distribution to construct a confidence interval for the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find tα/2,df for the following scenarios. (You may find it useful to reference the t table. Round your answers to 3 decimal places.)
a. | A 90% confidence level and a sample of 13 observations. | |
b. | A 95% confidence level and a sample of 13 observations. | |
c. | A 90% confidence level and a sample of 22 observations. | |
d. | A 95% confidence level and a sample of 22 observations. | |
Solution :
Using t table,
(a)
sample size = n = 13
Degrees of freedom = df = n - 1 = 12
t /2,df = t0.05,12 = 1.782
(b)
sample size = n = 13
Degrees of freedom = df = n - 1 = 12
t /2,df = t0.025,12 = 2.179
(c)
sample size = n = 22
Degrees of freedom = df = n - 1 = 21
t /2,df = t0.05,21 = 1.721
(d)
sample size = n = 22
Degrees of freedom = df = n - 1 = 21
t /2,df = t0.025,21 = 2.080
We use the t distribution to construct a confidence interval for the population mean when the...
We use the t distribution to construct a confidence interval for the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find tα/2,df for the following scenarios. (You may find it useful to reference the t table. Round your answers to 3 decimal places.) tα/2,df a. A 90% confidence level and a sample of 25 observations. b. A 95% confidence level and a sample of 25 observations.
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