Question

Use the normally distributed data below to develop the rcquested intervals. For each problem, clearly show the necessary critical value(s), a portion of the calculation steps, the final answer, and an interpretation of the interval. 46.4 43 49.6 45.7 46.8 52.8 37.4 1. Create a two-sided 95% CI for the standard deviation. (Usually, you would use a Normal Probability Plot to test the assumption of normality before constructing the interval, but we already know the data are normal.) cs canned wyith. Create a two-sided 95% CI for the mean. Assume the standard deviation is known to be 5.0. CamScanner

Answer 1

(1)

From the given data, the following statistics are calculated:

n = Sample Size = 7

= Sample mean =45.9571

s = Sample Standard Deviation = 4.8826

= 0.05

ndf = n - 1= 7 - 1 = 6

Confidence Interval:

Low End:
From Table:

Low End:

High End:

From table:

= 1.2373

High End:

Confidence Interval:

3.1463 < < 10.7519

(2)
SE = /

= 5.0/

= 1.8898

= 0.05

ndf = n - 1= 7 - 1= 6

From Table, critical values of t = 2.4469

Confidence Interval:

45.9571 (2.4469 X 1.8898)

= 45.9571 4.6242

= (41.3329 ,50.5813)

Confidence Interval:

41.3329 < <   50.5813