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1. Let a random sample of size 17 from a normal population for which both mean μ and variance σ2 are unknown yield x = 3.12 and s2 = 1.04. Determine a 99% con?dence interval for μ.
2. A random sample from a normal population yields the following 25 values:
90
87
121
96
106 107 89
107 83 92
117
93
98
120
97 109 78
87 99 79
104
85
91
107
89
(a) Calculate an unbiased estimate θˆ of the population mean.
(b) Give approximate 99% con?dence interval for the population mean.
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Samples of size 49 are taken from a population with a σ of 17. If the mean of the sample is 25, what is the confidence interval at the 90% confidence level?
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