Question

Measurements were made of the milk fat content (in percent) in six brands of feta cheese (a variety of goat cheese), with the following results. Assume that the population is normally distributed.

16.7, 20.1, 19.6, 21.7, 22.0, 23.9
Construct a 90% confidence interval for the population standard deviation σ.

Answer 1

To find the 90% confidence interval for the population standard deviation of milk fat content in feta cheese, calculate the sample standard deviation.

Step-by-step explanation:

To construct a 90% confidence interval for the population standard deviation σ of the milk fat content in brands of feta cheese, we will use the sample standard deviation and the chi-square distribution since the population standard deviation is unknown and the sample size is small. First, calculate the sample variance and standard deviation.

Then, use the chi-square distribution with degrees of freedom (df) equal to n - 1, where n is the sample size, to find the chi-square values that correspond to the lower and upper tail of the 90% confidence interval. The confidence interval for the population variance will be calculated using the formula ((n-1)s^2)/χ^2, where s is the sample standard deviation and χ^2 is the chi-square statistic. Finally, take the square root of the confidence interval for the variance to find the interval for the standard deviation.