Question

Calendar Gradebook essment e Intervals Due Sat 03/28/2020 11:00 pm You must estimate the mean temperature in degrees Fahrenheit) with the following sample temperatures: 98.8 50.3 83.3 67.3 77.1 78.7 Find the 80% confidence interval. Enter your answer as an open-interval (l.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 80% C.I. - Answer should be obtained without any preliminary rounding. Points possible: 4 Unlimited attempts. Submit

Answer 1

First let us fine mean and standard deviation

x = = 75.92

Create the following table.

data	data-mean	(data - mean)2
98.8	22.8833	523.64541889
50.3	-25.6167	656.21531889
83.3	7.3833	54.51311889
67.3	-8.6167	74.24751889
77.1	1.1833	1.40019889
78.7	2.7833	7.74675889

Find the sum of numbers in the last column to get.

Σ(xi - X)2 = 1317.7683

So standard deviaiton is

s= - V {(xi - x)2 = 16.23 n -1-5 16.23

Now let us assume that distribution is normal, so t value for 80% CI is TINV(0.2,5)=1.476

So Margin of Error is

E = + = 1.47610.25 = 9.78 V6

Hence CI is

CI = 1+E = 75.9249.78 = (66.14,85.7)