A random sample of n measurements was selected from a population with unknown me

Question

A random sample of n measurements was selected from a population with unknown mean mu and standard deviation sigmaequals=3535 for each of the situations in parts a through d. Calculate a 9090% confidence interval for mu for each of these situations.
a. n=7070, x overbarx=2929
b. n=200200, x overbarx=110110
c. n=9090, x overbarx=1414

d. ne=9090, x overbarx=4.534.53

e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a through d? Explain.

Explanation / Answer

Here z=1.645 as all n>30. Also given sd=35

We will calculate Margin of error for all case and compute CI as mu+/-E

a. E=sd*z/sqrt(n)=6.88

CI=29+/-6.88=(22.12,35.88)

b. E=5.49

CI=(194.51,205.49)

c. E=6.07

CI=(83.93,96.07)

d. E=6.07

CI=(-1.54,10.6)

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