The test marks for 29 students studying STSA 1624 produced a mean of 72,8% and a variance of 275,56%. If the distribution of the marks may be assumed to be approximately normally distributed, determine the upper limit, if a 99% confidence interval is set up for the population variance for the population of 1700 registered students.
To determine the upper limit for the 99% confidence interval for the population variance, we first need to find the critical value for a chi-square distribution with 28 degrees of freedom.
The degrees of freedom is calculated by subtracting 1 from the sample size (29 - 1 = 28).
The critical value for a 99% confidence interval with 28 degrees of freedom is found using a chi-square table or calculator. It is approximately 49.645.
Next, we calculate the upper limit using the formula:
Upper Limit = (n - 1) * sample variance / critical value
Where n is the sample size and the sample variance is given as 275.56%.
Plugging in the values:
Upper Limit = (29 - 1) * 275.56% / 49.645
= 28 * 2.7556 / 49.645
= 1.543088
Therefore, the upper limit for the 99% confidence interval for the population variance is approximately 1.543088.
To determine the upper limit of the 99% confidence interval for the population variance, we can use the chi-square distribution.
First, let's find the degrees of freedom (df) for the population variance calculation.
The degrees of freedom for the population variance is given by (n - 1), where n is the number of samples.
In this case, n = 29, so the degrees of freedom is 29 - 1 = 28.
Next, we need to find the critical chi-square value corresponding to a confidence level of 99% and df of 28.
To find this value, we can use statistical tables or a calculator.
Using a calculator, the critical chi-square value is approximately 48.394.
The upper limit of the 99% confidence interval for the population variance is calculated using the formula:
upper limit = ((n - 1) * sample variance) / critical chi-square value
In this case, the sample variance is 275.56% (0.2756 in decimal form), and the critical chi-square value is 48.394.
Plugging in the values:
upper limit = ((29 - 1) * 0.2756) / 48.394
upper limit = (28 * 0.2756) / 48.394
upper limit = 7.7224 / 48.394
upper limit ≈ 0.1596
Therefore, the upper limit of the 99% confidence interval for the population variance is approximately 0.1596.