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. (Round your answers to 3 decimal places.) t/2,df

a. A 95% confidence level and a sample of 16 observations.

b. A 90% confidence level and a sample of 16 observations.

c. A 95% confidence level and a sample of 7 observations.

d. A 90% confidence level and a sample of 7 observations.

Explanation / Answer

( a )

Level of confidence = 95%

Level of significance = 100% - 95% = 5%

Sample size = 16

Degrees of freedom = 16 – 1 = 15

By using t-distribution table we get t (a/2) is 2.131

( b )

Level of confidence = 90%

Level of significance = 100% - 90% = 10%

Sample size = 16

Degrees of freedom = 16 – 1 = 15

By using t-distribution table we get t (a/2) is 1.753

( c )

Level of confidence = 95%

Level of significance = 100% - 95% = 5%

Sample size = 7

Degrees of freedom = 7 – 1 = 6

By using t-distribution table we get t (a/2) is 2.447

( d )

Level of confidence = 90%

Level of significance = 100% - 90% = 10%

Sample size = 7

Degrees of freedom = 7 – 1 = 6

By using t-distribution table we get t (a/2) is 1.753

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