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.
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.
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1 answer