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natka813 [3]
3 years ago
13

Find the appropriate percentile from a​ t-distribution for constructing the following confidence interval.

Mathematics
1 answer:
Lina20 [59]3 years ago
8 0

Answer: 9.9248

Step-by-step explanation:

We know that the critical t- value for confidence interval is a two-tailed value from the t-distribution table corresponding to degree of freedom (df = n-1 , where n is the sample size) and the significance level (\alpha/2) .

The given confidence interval = 99%

⇒ Significance level = \alpha=100\%-99\%=1\%=0.01

Sample size : n=3

DEgree of freedom : df = n-1 = 2

Then, the  critical t- value for 99% confidence interval will be;

t_{\alpha/2, df}=t_{0.01/2,\ 2}

t_{0.005 , 2}=\pm9.9248   [From t-distribution table]

Hence, the appropriate percentile from a​ t-distribution for constructing the 99​% confidence interval with n = 3 is 9.9248.

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