5. The following data are known to be Gaussian: 88.1, 100, 91.1, 84.2, 92, 68.6,

Question

5. The following data are known to be Gaussian: 88.1, 100, 91.1, 84.2, 92, 68.6,79.4, 78.4,79.5, 94.8, 76.4, 76.7, 77.3, 106, 86.1, 87.1, 88.3, 88.5, 84.0, 67.9, 95.2, 74.1, 87.2, 84, 68.5. (a) Calculate the sample mean and standard deviation. (b) Construct an interval estimate of the mean and of the standard deviation with a confidence level of 95%. (c) Suppose one wants to estimate the mean of the process that generated the set of data above with an accuracy of ±0.1 at a confidence level of 98%. How many more samples of the process do we need?

Explanation / Answer

Ans:

a)sample mean=84.14

sample std dev=9.66

b)n=25

df=25-1=24

t value for 95% CI is 2.064

95% CI

=84.14+/-2.064*9.66/sqrt(25)

=84.14+/-3.99

=(80.15,88.13)

c)

n=(2.33*9.66/0.1)2=50660

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