The critical value that is appropriate for a 99% confidence level where n17, is unknown, and the population appears to be normally distributed is 2.921 (Option B).
A Critical value is the value of the test statistic that establishes the upper and lower boundaries of a confidence interval or the statistical significance threshold in a statistical test.
How did we arrive at the above conclusion?
We are given:
n=17, where n is the size of the set
df = n-1; (df means degree of freedom)
= 17-1
df = 16, at 99% confidence level.
Here we apply the t-test because the data is normally distributed.
∝ = 1-99% [Shere ∝ is the significance level)
= 0.01
∝/2 = 0.01/2
= 0.005
hence,
[tex]t_{\alpha /2} ,df[/tex] = [tex]t_{0.005}[/tex], 16 = 2.921. this is derived using the T-Table.
The above leads us to conclude therefore that Option B is correct.
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