We use the t distribution to construct a confidence interval for the population

Question

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 t2,df for the following scenarios. Use Table 2. (Round your answers to 3 decimal places.) t/2,df              a. A 90% confidence level and a sample of 20 observations.   b. A 95% confidence level and a sample of 20 observations.   c. A 90% confidence level and a sample of 10 observations.   d. A 95% confidence level and a sample of 10 observations.

Explanation / Answer

a.
A 90% confidence level and a sample of 20 observations
where,
ta/2 = t-table value
level of significance, = 0.1
from standard normal table, two tailed value of |t /2| with n-1 = 19 d.f is 1.729

b.
A 95% confidence level and a sample of 20 observations.
where,
ta/2 = t-table value
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 19 d.f is 2.093

c.
A 90% confidence level and a sample of 10 observations
where,
ta/2 = t-table value
level of significance, = 0.1
from standard normal table, two tailed value of |t /2| with n-1 = 9 d.f is 1.833

d.
A 95% confidence level and a sample of 10 observations
where,
ta/2 = t-table value
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 9 d.f is 2.262

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.