Question

A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean is x⎯⎯ = 770 and the sample standard deviation is s = 25. Use T.INV in Excel to find the appropriate t-multiplier.

Answer 1

For α=0.01 and two-tailed test: t=2.8188

For α=0.025 and two-tailed test: t=2.4055

For α=0.05 and two-tailed test: t=2.0739

For α=0.10 and two-tailed test: t=1.7171

Explanation:

In this problem, we have to estimate the value of the statistic "t" of a sample of size n=23 (22 degrees of freedom), in which the sample mean is M=770 and the sample standard deviation is s=25.

The estimated standard deviation is

`s_M=s/√(N)=25/√(23) =5.21`

The critical values of the statistic t depends on the significance level:

The degree of freedom is known: df=22.

For α=0.01 and two-tailed test: t=2.8188

For α=0.025 and two-tailed test: t=2.4055

For α=0.05 and two-tailed test: t=2.0739

For α=0.10 and two-tailed test: t=1.7171