16. The registrar ar Miami State University does not know the average age of an
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Question
16. The registrar ar Miami State University does not know the average age of an undergraduate student at her university. In an effort to estimate it, she takes a random sample of 120 of their undergraduate students and asks them their age. She has no information about the population other than she assumes it is normally distributed. Which of the following best describes the statistical analysis she will be doing in this study? A. z confidence interval for a single population mean B. t confidence interval for a single population mean C. z test for single mean D. t test for single mean 17. Who is generally credited with having developed the tes? y D. Simeon Poisson A. Karl Gauss B. William Gosset C.W.C. HandExplanation / Answer
16.
option (B) is correct
because :
if X : age of undergraduate students of the university
it is assumed that X~N(m,sigma2)
m= population mean= average age
sigma = population standard deviation
if x bar and s denotes the sample mean and sample standard deviation respectively based on 120 (sample size n=120) observations,then
[(x bar -m0)/{(s/sqrt(n)}] follows t(n-1) distribution under the assumption that m=m0 (m0 is known or specified)
if we are to find the 95% confidence interval for population age m,then choosing alpha(probability of type 1 eorro)=0.05 we get
P[|(x bar -m0)/{(s/sqrt(n)}|<t0.025;(n-1)] =0.95
which implies
P[(x bar - t0.025;(n-1)) * (sqrt(n)/s) <m0 < (x bar + t0.025;(n-1))* (sqrt(n)/s)]= 0.95
in this way we find an interval of true population mean m0 to which the population mean (average age ) belongs with 95% probability.
17.
option (B)
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