Asample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. the chi-square values to be used for this interval estimation are

a. 16.151 and 40.113.

b. 14.573 and 43.195.

c. 15.308 and 44.461.

d. 11.808 and 49.645.

b. 14.573 and 43.195.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Solution to the problem

The confidence interval for the population variance is given by the following formula:

We need on this case to calculate the critical values. First we need to calculate the degrees of freedom given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table for the Chis square distribution with 27 degrees of freedom to find the critical values. We need a value that accumulates 0.025 of the area on the left tail and 0.025 of the area on the right tail.  

The excel commands would be: "=CHISQ.INV(0.025,27)" "=CHISQ.INV(0.975,27)". so for this case the critical values are:

b. 14.573 and 43.195.

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x