Question

In: Statistics and Probability

Professor Venkat is on a mission to find out the average number of students absent from...

Professor Venkat is on a mission to find out the average number of students absent from his lectures. For this, he analyzed 14 random attendance sheets from his previous semesters and found out that on average, the number of absentees was 38 with a standard deviation of 12. Let's assume that the data follows a Gaussian distribution. Construct a 99% confidence interval for the true mean of the dataset.

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 38

sample standard deviation = s = 12

sample size = n = 14

Degrees of freedom = df = n - 1 = 13

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,24 = 3.012

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 3.012 * (12 / $\sqrt$ 14)

= 9.660

The 99% confidence interval estimate of the population mean is,

- E < < + E

38 - 9.660 < < 38 + 9.660

28.340 < < 47.660

A 99% confidence interval for the true mean of the dataset is ,

(28.340 , 47.660)

orchestra answered 2 years ago

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