4. We use the t distribution when we don\'t know the underlying distribution (st

Question

4. We use the t distribution when we don't know the underlying distribution (standard deviation and mean). If we assume, though, that the underlying population is normally distributed we can use the t distribution in small samples (without needing to apply the Central Limit Theorem directly). For each of the following, assuming underlying normality, find tidf for the following scenarios a, b, c, d, e. 90% confidence level with a sample of 28 observations 90% confidence level with a sample of 15 observations 95% confidence level with a sample of 28 observations 95% confidence level with a sample of 15 observations In words, what can we say about the roll sample size plays in the size of our confidence intervals?

Explanation / Answer

a) Degrees of freedom = n - 1 = 28 - 1 = 27

So,

Critical value = 1.7033           [Rounded off to 4 decimal places]

b) Degrees of freedom = n - 1 = 15 - 1 = 14

So,

Critical value = 1.7613           [Rounded off to 4 decimal places]

c) Degrees of freedom = n - 1 = 28 - 1 = 27

So,

Critical value = 2.0518           [Rounded off to 4 decimal places]

d) Degrees of freedom = n - 1 = 28 - 1 = 27

So,

Critical value = 2.1448           [Rounded off to 4 decimal places]

e) As we increase the sample size by keeping confidence level constant, the critical value decreases and so the width of the confidence interval decreases.

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