Assuming a sample size of 31: a) What t-scores isolate the middle 95% of the population?...

Assuming a sample size of 31:
1. a) What t-scores isolate the middle 95% of the population?
2. b) What t-scores isolate the middle 99% of the population?
Assuming a sample size of 22:
1. a) What t-scores isolate the middle 95% of the population?
2. b) What t-scores isolate the middle 99% of the population?

Expert Solution

$P(t > b) = 0.025 \\ or,\ P(t > b) = P(t > 2.042) \hspace{10 mm}[$ From t table with one tail probability \\ \hspace*{60 mm} of 0.025 and df = 30 $] \\ or, b = 2.042 \\\\ $ As, t distribution is symmetric about t = 0, so a = -2.042 $ \\\\ $ So, the scores of $ \mathbf{-2.042\ and\ 2.042} $ isolate the middle 95\% of the population $$

$P(t > b) = 0.025 \\ or,\ P(t > b) = P(t > 2.080) \hspace{10 mm}[$ From t table with one tail probability \\ \hspace*{60 mm} of 0.025 and df = 21 $] \\ or, b = 2.080 \\\\ $ As, t distribution is symmetric about t = 0, so a = -2.080 $ \\\\ $ So, the scores of $ \mathbf{-2.080\ and\ 2.080} $ isolate the middle 95\% of the population $$

orchestra answered 2 years ago

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Assuming a sample size of 31: a) What t-scores isolate the middle 95% of the population?...

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