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Chapter 8: Q96E (page 452)

A random sample of n = 6 observations from a normal distribution resulted in the data shown in the table. Compute a 95% confidence interval for 蟽2

Short Answer

Expert verified

The 95% confidence interval for 蟽2is (4, 2689, 65.9044).

Step by step solution

01

Given information

Given data is as follows,

8 2 3 7 11 6

02

Calculating the Confidence interval

The 95% confidence interval can be calculated using the formula,

n-1s2蠂伪22猢�蟽2猢�n-1s2蠂1-伪22

From the given data, n=6ands=3.31

From the table values, at the 0.05 level of significance and 5 degrees of freedom, the value for 5 is 12.832 and

the value forn-1s2蠂0.0052猢�蟽2猢�n-1s2蠂0.9952=100-162140.169猢�蟽2猢�100-16267.3276 is 0.8312.

Substitute the values to get the required confidence interval

6-13.31212.8325猢�蟽2猢�6-13.3120.83124.2689猢�蟽2猢�65.9044

Therefore, the 95% confidence interval for蟽2is (4, 2689, 65.9044).

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