Question

You randomly select and measure the contents of bottles of cough syrup. The results​ (in fluid​ ounces) are shown to the right 4.211

4.298
4.258
4.242
4.182
4.243
4.266
4.243
4.226
4.234
Construct a 90% confidence interval for the population variance based on the given sample data.
a. 0.0002 to 0.0005
b. 0.0001 to 0.0003
c. 0.0003 to 0.0006
d. 0.0002 to 0.0004

Answer 1

To construct a 90% confidence interval for the population variance based on the given sample data, calculate the sample variance and use the chi-squared distribution. The confidence interval is 0.0002 to 0.0004.

Step-by-step explanation:

To construct a confidence interval for the population variance, we can use the chi-squared distribution. Given the sample data, we first need to find the sample variance, which is the sum of the squared differences between each measurement and the sample mean divided by the sample size minus one. Next, we can calculate the upper and lower limits of the confidence interval using the chi-squared distribution with degrees of freedom equal to the sample size minus one. The formula for the confidence interval is:

Lower Limit = (n - 1) * S^2 / chi2_upper

Upper Limit = (n - 1) * S^2 / chi2_lower

Based on the given sample data, the 90% confidence interval for the population variance is ranging from 0.0002 to 0.0004.