Question

In: Statistics and Probability

We have the following sample observations: 9.8, 9.43, 8.97, 9.33, 9.14, 9.55 a). Derive a 90%...

We have the following sample observations: 9.8, 9.43, 8.97, 9.33, 9.14, 9.55

a). Derive a 90% CI for the population variance. First come up with a pivotal expression, then use that pivotal along with the sample data to generate the confidence interval.

b). Derive a 95% CI for the population mean. First come up with a pivotal expression, then use that pivotal along with the sample data to generate the confidence interval.

Expert Solution

From the given data,

= 9.37 , S = 0.2951 , S² = 0.08708

a)

90% confidence interval for is

(n-1) S² / /2 < < (n-1) S² / 1-/2

(6-1) * 0.08708 / 11.070 < < ( 6 - 1) * 0.08708 / 1.145

0.0393 < < 0.3803

90% CI is ( 0.0393 , 0.3803)

b)

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

9.37 - 2.571 * 0.2951 / sqrt(6) < < 9.37 + 2.571 * 0.2951 / sqrt(6)

9.0603 < < 9.6797

95% CI is ( 9.0603 , 9.6797)

orchestra answered 2 years ago

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