Do one of the following as appropriate a Find the critical v

Do one of the following, as appropriate. (a) Find the critical value Za/ 2, (b) find the critical value ta/2, (c) state that neither the normal nor the t distribution applies. Confidence level 98%; n = 25; sigma is known; population appears to be very skewed.

Find the critical value.

Solution

(a) find the critical value za/2.

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Why? Although the population is very skewed, when we get the sampling distrbution, by central limit theorem, the distrbution of the sample mean will be approximately normal. Also, sigma is known, so we use z instead of t.

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Thus,

As

alpha/2 = (1-confidence level)/2 = (1-0.98)/2 = 0.01,

zcrit = z(alpha/2) = z(0.01) = 2.326347874 [ANSWER]