The following information is obtained from a sample. Assume the standard deviati

Question

The following information is obtained from a sample. Assume the standard deviation of the population is known n= 650 x = 1.05 sigma = 5.22 Construct a 95% confidence interval for mu. Out of a sample of 500 college students at colleges and universities in San Antonio, 223 said it was "very difficult" or "nearly impossible" to find affordable rent within four miles of their respective schools. a) Construct a 90% confidence Interval for the proportion of all college students in San Anto who think this way

Explanation / Answer

The 95% c.i=Xbar+-Z (sigma/sqrt N), where, Xbar is sample mean, sigma is population standard deviation and N is sample size.

95% c.i=1.05+-1.96(5.22/sqrt 650)

=0.65 to 1.45

The 90% c.i= Ps+-Z sqrt [Pu(1-Pu)/N], where, Ps is sample proportion, Pu is population proportion and N is sample size.

90% c.i=223/500+-1.65 sqrt [0.5(1-0.5)/500]

=0.41 to 0.48

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