Question

PLEASE HELP! 50 POINTS! Consider the following set of sample data: (34, 32, 34, 32, 40, 37, 31, 31, 29, 27). Which of the following will give a 95% t confidence interval for the mean of the population from which the sample was drawn?

Answer 1

(15.23,41.016)

Explanation:

WE must determine the mean of the data set: Which is the sum of the set divided by the number in the set.

`= (21 + 24 + 25 + 32 + 35 + 31 + 29 + 28)/8 = 225/8 = 28.125`
We must also determine the standard deviation: Which is the square root of the variance and the variance is the sum of squares of the sample number minus the mean divided by the number if the set data:

`= ((21 - 28.125)^(2) + (24 - 28.125)^(2) +(25 - 28.125)^(2) + (32 - 28.125)^(2) + (35 - 28.125)^(2) + (31 - 28.125)^(2) + (29 - 28.125)^(2) (28 - 28.125)^(2)`

`= 148.877/8 = 18.6`
The 95% confidence interval is defined as: The mean ± 1.96*standard deviation divided by the sqaure root of the number of data in the set:

`= 28.125 + (1.96 *18.6)/(√(8) )`

`= 41.016`

`= 28.125 - (1.96 * 18.6)/(√(8)) = 15.23`
The confidence interval for this data set is (15.23,41.016)

Answer 2

32.7 ± 2.262(1.19)

Explanation:

See attached pictures