High School

Interpret the results.

(a) What is the confidence interval for the population variance? (Round to two decimal places as needed.)

The number of hours of reserve capacity of 10 randomly selected automotive batteries is recorded.

Answer :

The 95% confidence interval for the population variance is [0.02, 0.23].

Calculating the confidence interval for the population variance?

From the question, we have the following parameters that can be used in our computation:

The table of values

Calculate the sample mean and sample variance as follows

Sample mean = (1.74 + 1.84 + 1.53 + 1.62 + 1.78 + 1.95 + 1.37 + 1.55 + 1.42 + 2.04) / 10 = 1.68

Sample variance = (0.003136 + 0.024336 + 0.023716 + 0.004096 + 0.009216 + 0.070756 + 0.098596 + 0.017956 + 0.069696 + 0.126736) / 10 = 0.044824

Calculate the degrees of freedom.

Degrees of freedom = n - 1

df = 10 - 1 = 9

For a 95% confidence interval, the chi-squared values are 1.7345 and 16.9190.

So, we have

Limit = (degrees of freedom * sample variance) / chi-squared value

This gives

Lower limit = (9 * 0.044824) / 16.9190 = 0.02

Upper limit = (9 * 0.044824) / 1.7345 = 0.23

Hence, the 95% confidence interval for the population variance is [0.02, 0.23].

Read more about confidence interval at

https://brainly.com/question/20309162

#SPJ4

Question

The number of hours of reserve capacity of 10 randomly selected automotive batteries is shown to the right. Assume the sample is taken from a normally distributed population.

What is the confidence interval for the population variance? (Round to two decimal places as needed)

X (X-Xbar)^2

1.74 0.003136

1.84 0.024336

1.53 0.023716

1.62 0.004096

1.78 0.009216

1.95 0.070756

1.37 0.098596

1.55 0.017956

1.42 0.069696

2.04 0.126736

Total 16.84 0.44824

Other Questions