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1 . Suppose a 95% confidence interval for the mean is (10, 12) when you know the value of the population standard deviation (sigma). If you HAD NOT KNOWN the value of sigma, would your confidence interval have been wider, narrower, or the same?

 

2 . Suppose your hypotheses in a hypothesis test for the mean are Ho: u = 8 vs Ho: u > 8. Suppose your test statistic using Z is 2.13 and you knew the value of the population standard deviation. If you HAD NOT KNOWN the value of the population standard deviation, would your test statistic using t have been greater, smaller, or the same? 

 

3 . (T/F) There are situations where if you had known the population standard deviation you could have rejected Ho, but since you did not know it, you ended up failing to reject Ho.