Construct 98% confidence intervals for the a) population variance and the b)population standard deviation **Confidence Interval for Population Variance and Standard Deviation**The data represents the reserve capacity hours of 10 randomly selected automotive batteries:- 1.71, 1.87, 1.58, 1.61, 1.78- 1.98, 1.36, 1.58, 1.47, 2.05**Instructions:**Given that the sample is from a normally distributed population, we need to construct a 98% confidence interval for:(a) The population variance $\sigma^2$(b) The population standard deviation $\sigma$**Tasks:**(a) Determine the confidence interval for the population variance and fill in the blanks. Round answers to three decimal places as necessary.

Use STDEV function in excel to find the standard deviation. Then, s=0.2215. And the variance is s2=0.22152=0.04906At 98% level,α=1-98%=1-0.98=0.02 AndThe degree of freedom=n-1=10-1=9The critical values areχ2α,n-1=χ20.02,9=19.679 Andχ21-α,n-1=χ20.98,9=2.5324The 98% confidence interval for variance is n-1s2χ2α,n-1≤σ2≤n-1s2χ21-α,n-1=90.0490619.679≤σ2≤90.049062.5324=0.4415419.679≤σ2≤0.441542.5324=0.022≤σ2≤0.174 The 98% confidence interval for standard deviation is n-1s2χ2α,n-1≤σ≤n-1s2χ21-α,n-1=0.022≤σ≤0.174=0.150≤σ≤0.417

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Probability

The number of hours of reserve capacity of 10 randomly selected automotive batteries is shown to the right. 1.71 1.87 1.58 1.61 1.78 1.98 1.36 1.58 1.47 2.05 Assume the sample is taken from a normally distributed population. Construct 98% confidence intervals for (a) the population variance o2 and (b) the population standard deviation o. (a) The confidence interval for the population variance is ( ). (Round to three decimal places as needed.)

The number of hours of reserve capacity of 10 randomly selected automotive batteries is shown to the right. 1.71 1.87 1.58 1.61 1.78 1.98 1.36 1.58 1.47 2.05 Assume the sample is taken from a normally distributed population. Construct 98% confidence intervals for (a) the population variance o2 and (b) the population standard deviation o. (a) The confidence interval for the population variance is ( ). (Round to three decimal places as needed.)

A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Construct 98% confidence intervals for the a) population variance and the b)population standard deviation

**Confidence Interval for Population Variance and Standard Deviation**

The data represents the reserve capacity hours of 10 randomly selected automotive batteries:

- 1.71, 1.87, 1.58, 1.61, 1.78
- 1.98, 1.36, 1.58, 1.47, 2.05

**Instructions:**

Given that the sample is from a normally distributed population, we need to construct a 98% confidence interval for:

(a) The population variance $\sigma^2$

(b) The population standard deviation $\sigma$

**Tasks:**

(a) Determine the confidence interval for the population variance and fill in the blanks. Round answers to three decimal places as necessary.

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