Question 6 Compute a 95% confidence interval for the population mean, based on t

Question

Question 6 Compute a 95% confidence interval for the population mean, based on the sample numbers 21, 28, 33 34, 25, 26, and 135. What is the Critical value? (Get 4 decimal digits). Use the table here: http://www.statsoft.com/textbook/sttable.html Question 6 options C 2.5706 C 3.7074 2.4469 C 2.3646 Question 7 Compute a 95% confidence interval for the population mean, based on the sample numbers 21, 28, 33. 34, 25, 26, and 135. What is the margin of error? (Round to two decimal digits) Question 7 options: 29.57 37.69 38.80 41.83

Explanation / Answer

Question 6

Here mean=Sumx/n=43.1429

and for sd

Create the following table.

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

(xiX¯)2=9966.8571

Calculate using the above formula.

=((xiX¯)^2/n1)=(9966.8571/71)40.7571

Using t table value we get Critical value as 2.447 for 6 df i.e. n-1=7-1 df

Question 7

Margin of error=t*sd/sqrt(n)=2.447*40.7571/sqrt(7)=37.6954

Question 8

Lower bound =mean-E=43.1429-37.6954=5.449

Upper bound=mean+E=80.837

Question 9

Changing the data we get mean=27.7143 and sd=4.5356

t remains same

E=2.447*4.5356/sqrt(7)=4.1949

CI=27.7143+/-4.1949=(23.5194,31.909)

data data-mean (data - mean)2 21 -22.1429 490.30802041 28 -15.1429 229.30742041 33 -10.1429 102.87842041 34 -9.1429 83.59262041 25 -18.1429 329.16482041 26 -17.1429 293.87902041 135 91.8571 8437.72682041

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